Solid Geometry — MCQ | প্রশ্ন করি

Chapter 13

Solid Geometry

152 questions · 19 sections

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1.Basic Concepts9

Q 1C-13-Q001medium

Each of length, breadth and height of a body is called what?

adimension
baxis
ccoordinate
dmagnitude

Q 2C-13-Q002medium

A point is which of the following?

aone-dimensional
btwo-dimensional
cthree-dimensional
dzero-dimensional

Q 3C-13-Q003medium

For practical purpose, a point is indicated by what?

aa small circle
ba dot
ca cross
da tiny line

Q 4C-13-Q004medium

A line is how many dimensional?

azero
bone
ctwo
dthree

Q 5C-13-Q005medium

A surface has which of the following?

alength only
blength and breadth
clength, breadth and height
dheight only

Q 6C-13-Q006medium

A surface is how many dimensional?

azero-dimensional
bone-dimensional
ctwo-dimensional
dthree-dimensional

Q 7C-13-Q007medium

A body having length, breadth and height is called what?

asurface
bline
csolid
dplane

Q 8C-13-Q008medium

A solid is how many dimensional?

aone
btwo
cthree
dfour

Q 9C-13-Q009combomedium

Consider the following statements:

a point has no dimension
a line has length only
a surface has length, breadth and height

ai and ii
bi and iii
cii and iii
di, ii and iii

2.Some Elementary Definitions22

Q 1C-13-Q010medium

If the straight line joining any two points on a surface lies wholly on that surface, the surface is called what?

acurved surface
bplane surface
coblique surface
dspherical surface

Q 2C-13-Q011medium

Which of the following is an example of a plane surface?

asurface of a sphere
bsurface of a cone
cupper surface of still water of a pond
dsurface of a cylinder

Q 3C-13-Q012medium

The surface of a sphere is what kind of surface?

aplane surface
bflat surface
ccurved surface
ddihedral surface

Q 4C-13-Q013medium

The branch of mathematics that deals with the properties of solids, surfaces, lines and points is called what?

aplane geometry
bsolid geometry
ctrigonometry
danalytic geometry

Q 5C-13-Q014medium

Solid geometry is also known as what?

ageometry of one dimension
bgeometry of two dimensions
cgeometry of three dimensions
dgeometry of zero dimension

Q 6C-13-Q015medium

Two or more straight lines that lie in the same plane are called what?

askew lines
bcoplanar straight lines
cperpendicular lines
doblique lines

Q 7C-13-Q016medium

Straight lines that do not lie in one plane are called what?

acoplanar lines
bparallel lines
cskew or non-coplanar lines
dconcurrent lines

Q 8C-13-Q017medium

Two pencils tied cross-wise like a plus sign represent which type of lines?

aparallel lines
bcoplanar lines
ccoincident lines
dnon-coplanar lines

Q 9C-13-Q018medium

Two coplanar straight lines that do not intersect each other are called what?

askew lines
bparallel straight lines
cperpendicular lines
dintersecting lines

Q 10C-13-Q019medium

Two planes are said to be parallel when they have how many common points?

aexactly one
bexactly two
cinfinitely many
dnone

Q 11C-13-Q020medium

A straight line is said to be parallel to a plane when they have how many common points (even when extended indefinitely)?

aone
btwo
cnone
dinfinitely many

Q 12C-13-Q021medium

A straight line is normal (perpendicular) to a plane when it is perpendicular to which of the following?

aonly one straight line in the plane
bonly the boundary of the plane
cevery straight line in the plane that meets it
dno line in the plane

Q 13C-13-Q022medium

A straight line which is neither parallel nor perpendicular to a plane is called what?

anormal line
bparallel line
coblique line
dvertical line

Q 14C-13-Q023medium

A straight line or plane is said to be vertical when it is parallel to what?

athe horizon
ba freely hanging plumb line at rest
cthe ground
dan oblique line

Q 15C-13-Q024medium

A plane is said to be horizontal when it is what?

aparallel to a vertical line
bperpendicular to a vertical line
cparallel to itself
dinclined to a vertical line

Q 16C-13-Q025medium

A quadrilateral whose four sides lie in the same plane is called what?

askew quadrilateral
bplanar quadrilateral
ccyclic quadrilateral
dtangential quadrilateral

Q 17C-13-Q026medium

In a skew quadrilateral, two adjacent sides lie in one plane and the other two adjacent sides lie in what?

athe same plane
banother plane
ca perpendicular plane
dno plane at all

Q 18C-13-Q027medium

The angle between two skew straight lines is found by drawing through any point lines parallel to which of the following?

aonly one of them
bneither of them
cboth of them
da perpendicular to both

Q 19C-13-Q028medium

If two planes intersect in a straight line, the angle between two lines drawn from any point on the intersection line, each perpendicular to it and lying in each plane, is called what?

asolid angle
bplane angle
cdihedral angle
doblique angle

Q 20C-13-Q029medium

Two intersecting planes are perpendicular to each other when the dihedral angle between them is what?

aan acute angle
ba right angle
can obtuse angle
da straight angle

Q 21C-13-Q030medium

The projection of a point on a given plane is what?

athe centre of the plane
bthe foot of the perpendicular drawn from the point to the plane
cthe nearest vertex of the plane
dthe midpoint of the plane

Q 22C-13-Q031medium

The orthogonal projection of a curved line on a plane is which of the following?

aalways a straight line
balways a point
cthe locus of feet of perpendiculars from all points of the line to the plane
dalways a circle

3.Relation between two straight lines2

Q 1C-13-Q032medium

Two coplanar straight lines must either be parallel or which of the following?

aintersect at infinitely many points
bmeet in a point
ccoincide entirely
dbe skew

Q 2C-13-Q033medium

Two skew straight lines neither meet in a point nor are what?

acoplanar
bparallel
cequal
dperpendicular

4.Axioms3

Q 1C-13-Q034medium

A straight line joining any two points in a plane lies where?

apartly outside the plane
bwholly in that plane
cperpendicular to the plane
dparallel to the plane

Q 2C-13-Q035medium

If a straight line and a plane have two common points, then they have how many common points?

aexactly two
bexactly three
cinnumerable common points along the line
dexactly four

Q 3C-13-Q036medium

Through one or two given straight lines, how many planes can be drawn?

aexactly one
bexactly two
cinfinite
dnone

5.Relation between a straight line and a plane2

Q 1C-13-Q037medium

If a straight line cuts a plane, how many common points do they have?

azero
bone and only one
cexactly two
dinfinitely many

Q 2C-13-Q038medium

If a straight line and a plane have two common points, then the line will do what?

acompletely coincide with the plane
bbe parallel to the plane
cbe perpendicular to the plane
dtouch the plane at one point

6.Relation between two planes1

Q 1C-13-Q039medium

If two planes intersect each other, they intersect along what?

aa curve
ba single point
ca straight line
da parabola

7.Solid5

Q 1C-13-Q040medium

The body enclosed by plane or curved surfaces and occupying some space is called what?

asurface
bsolid
cline
dregion

Q 2C-13-Q041medium

At least how many planes are required to enclose some space?

atwo
bthree
cfour
dfive

Q 3C-13-Q042medium

The line in which two planes of a solid intersect is called what?

aface
bvertex
cedge
ddiagonal

Q 4C-13-Q043medium

A book or a brick has how many faces and how many edges respectively?

a4 and 8
b6 and 12
c8 and 12
d6 and 8

Q 5C-13-Q044medium

A cricket ball is enclosed by what type of surface?

aplane surface
bcurved surface
cpolygonal surface
dflat surface

8.Volume and area of surface of uniform solids5

Q 1C-13-Q045medium

The solid enclosed by three pairs of parallel planes is called what?

aprism
bpyramid
cparallelepiped
dcone

Q 2C-13-Q046medium

Each face of a parallelepiped is what kind of figure?

atriangle
bparallelogram
ctrapezium
drhombus only

Q 3C-13-Q047medium

A parallelepiped has how many edges, divided into how many groups?

a12 edges in 3 groups
b12 edges in 4 groups
c8 edges in 2 groups
d6 edges in 3 groups

Q 4C-13-Q048medium

A parallelepiped whose six faces are all rectangles is called what?

acube
brectangular parallelepiped
cprism
dpyramid

Q 5C-13-Q049medium

A rectangular parallelepiped whose six faces are all squares is called what?

acube
bcuboid
cprism
dtetrahedron

9.Rectangular Parallelepiped6

Q 1C-13-Q050medium

If the length, breadth and height of a rectangular parallelepiped are $a, b, c$ , the area of its whole surface is which of the following?

a $abc$
b $2(ab + bc + ca)$
c $a^2 + b^2 + c^2$
d $\sqrt{a^2+b^2+c^2}$

Q 2C-13-Q051medium

The volume of a rectangular parallelepiped of dimensions $a, b, c$ is which of the following?

a $a + b + c$
b $2(ab+bc+ca)$
c $abc$
d $a^2bc$

Q 3C-13-Q052medium

The length of a diagonal of a rectangular parallelepiped of dimensions $a, b, c$ is which of the following?

a $a+b+c$
b $\sqrt{a^2+b^2+c^2}$
c $\sqrt{ab+bc+ca}$
d $\sqrt{abc}$

Q 4C-13-Q053medium

The length, breadth and height of a rectangular parallelepiped are in the ratio $4:3:2$ and the area of its whole surface is 468 square metres. What is the value of $x$ if the dimensions are $4x, 3x, 2x$ ?

Q 5C-13-Q054medium

The length, breadth and height of a rectangular parallelepiped are in the ratio $4:3:2$ and total surface area is 468 sq m. Its volume is which of the following?

a432 cubic m
b540 cubic m
c648 cubic m
d720 cubic m

Q 6C-13-Q055medium

For the parallelepiped of dimensions $12, 9, 6$ metres, the diagonal is approximately how many metres?

a15.00
b16.16
c18.00
d20.50

10.Cube6

Q 1C-13-Q056medium

The area of the whole surface of a cube of edge $a$ is which of the following?

a $a^2$
b $4a^2$
c $6a^2$
d $8a^2$

Q 2C-13-Q057medium

The volume of a cube of edge $a$ is which of the following?

a $a^2$
b $a^3$
c $6a^3$
d $\sqrt{3}a$

Q 3C-13-Q058medium

The length of the diagonal of a cube of edge $a$ is which of the following?

a $a\sqrt{2}$
b $a\sqrt{3}$
c $2a$
d $3a$

Q 4C-13-Q059medium

If the edge of a cube is 5 cm, its total surface area is which of the following?

a25 sq cm
b75 sq cm
c125 sq cm
d150 sq cm

Q 5C-13-Q060medium

If the edge of a cube is 4 cm, its volume is which of the following?

a16 cubic cm
b32 cubic cm
c64 cubic cm
d128 cubic cm

Q 6C-13-Q061combomedium

Consider the following formulas for a cube of edge $a$ :

surface area $= 6a^2$
volume $= a^3$
diagonal $= \sqrt{3}\, a$

ai and ii
bi and iii
cii and iii
di, ii and iii

11.Prism10

Q 1C-13-Q062medium

A prism is a polyhedron bounded by two parallel polygonal faces and other faces which are always what?

atriangles
bparallelograms
ctrapeziums
dcircles

Q 2C-13-Q063medium

The two parallel polygonal faces of a prism are known as what?

aapex faces
blateral faces
cbases
dedges

Q 3C-13-Q064medium

If all the lateral surfaces of a prism are rectangular, the prism is called what?

aoblique prism
bright prism
cregular prism
dirregular prism

Q 4C-13-Q065medium

Right triangular prism made of glass is used for what?

afocusing of light
breflection of light
cscattering (dispersion) of light
dpolarisation of light

Q 5C-13-Q066medium

The total surface area of a prism is given by which of the following?

a(area of base) + (perimeter of base $\times$ height)
b2(area of base) + (perimeter of base $\times$ height)
c(area of base) $\times$ height
d $\dfrac{1}{3}$ (area of base) $\times$ height

Q 6C-13-Q067medium

The volume of a prism is given by which of the following?

aperimeter of base $\times$ height
barea of base $\times$ height
c $\dfrac{1}{3}$ (area of base $\times$ height)
d $\dfrac{1}{2}$ (area of base $\times$ height)

Q 7C-13-Q068medium

The base of a triangular prism has sides 3, 4, 5 cm. What kind of triangle is the base?

aequilateral
bisosceles
cright-angled
dobtuse-angled

Q 8C-13-Q069medium

If the sides of the base of a triangular prism are 3, 4, 5 cm, the area of the base is which of the following?

a6 sq cm
b12 sq cm
c10 sq cm
d24 sq cm

Q 9C-13-Q070medium

A triangular prism has base sides 3, 4, 5 cm and height 8 cm. Its volume is which of the following?

a24 cubic cm
b36 cubic cm
c48 cubic cm
d60 cubic cm

Q 10C-13-Q071medium

A triangular prism has base sides 3, 4, 5 cm and height 8 cm. Total surface area is which of the following?

a60 sq cm
b96 sq cm
c108 sq cm
d120 sq cm

12.Pyramid14

Q 1C-13-Q072medium

A solid figure with a polygonal base and triangular faces meeting at a common point is called what?

aprism
bcylinder
cpyramid
dcone

Q 2C-13-Q073medium

A pyramid is called regular when its base is a regular polygon and its lateral faces are which of the following?

ascalene triangles
bcongruent triangles
cparallelograms
drectangles

Q 3C-13-Q074medium

A solid enclosed by four equilateral triangles is called what?

aregular tetrahedron
bcube
csquare pyramid
doctahedron

Q 4C-13-Q075medium

A regular tetrahedron has how many edges?

Q 5C-13-Q076medium

A regular tetrahedron has how many vertices?

Q 6C-13-Q077medium

The line joining the vertex of a pyramid to any corner of the base is called what?

aheight
bslant height
cedge of the pyramid
daxis

Q 7C-13-Q078medium

The length of the perpendicular from the vertex to the base of a pyramid is called what?

aslant height
bheight
capothem
dlateral edge

Q 8C-13-Q079medium

For a regular pyramid of height $h$ and inscribed-circle radius $r$ of the base, the slant height $l$ is which of the following?

a $h+r$
b $\sqrt{h^2-r^2}$
c $\sqrt{h^2+r^2}$
d $hr$

Q 9C-13-Q080medium

The volume of a pyramid is which of the following?

abase area $\times$ height
b $\dfrac{1}{2}$ base area $\times$ height
c $\dfrac{1}{3}$ base area $\times$ height
d $\dfrac{2}{3}$ base area $\times$ height

Q 10C-13-Q081medium

For a regular pyramid the area of all surfaces equals base area + which of the following?

a $\dfrac{1}{2}$ (perimeter of base $\times$ slant height)
bperimeter of base $\times$ height
cperimeter of base $\times$ slant height
d $\dfrac{1}{3}$ (perimeter $\times$ slant height)

Q 11C-13-Q082medium

A pyramid has a square base of side 10 cm and height 12 cm. The radius of the inscribed circle of the base is which of the following?

a4 cm
b5 cm
c6 cm
d10 cm

Q 12C-13-Q083medium

For a square-base pyramid of base side 10 cm and height 12 cm, the slant height of any lateral face is which of the following?

a12 cm
b13 cm
c14 cm
d15 cm

Q 13C-13-Q084medium

For a pyramid with square base of side 10 cm and height 12 cm, the area of all surfaces is which of the following?

a260 sq cm
b300 sq cm
c360 sq cm
d400 sq cm

Q 14C-13-Q085medium

The volume of a pyramid with square base of side 10 cm and height 12 cm is which of the following?

a360 cubic cm
b400 cubic cm
c480 cubic cm
d1200 cubic cm

13.Right circular cone12

Q 1C-13-Q086medium

A right circular cone is formed by a complete revolution of a right-angled triangle about which of the following as axis?

aits hypotenuse
bits longest side
cone of the sides adjacent to the right angle
dthe median from the right angle

Q 2C-13-Q087medium

The vertical angle of the right-angled triangle that is rotated to form a cone is called what for the cone?

abase angle
bsemi-vertical angle
capex angle
ddihedral angle

Q 3C-13-Q088medium

The area of the curved surface of a right circular cone of base radius $r$ and slant height $l$ is which of the following?

a $\pi r^2$
b $\pi r l$
c $\pi r (r+l)$
d $2\pi r l$

Q 4C-13-Q089medium

The total surface area of a right circular cone of base radius $r$ and slant height $l$ is which of the following?

a $\pi r l$
b $\pi r^2$
c $\pi r (r+l)$
d $\pi r (l-r)$

Q 5C-13-Q090medium

The volume of a right circular cone of base radius $r$ and height $h$ is which of the following?

a $\pi r^2 h$
b $\dfrac{1}{2}\pi r^2 h$
c $\dfrac{1}{3}\pi r^2 h$
d $\dfrac{2}{3}\pi r^2 h$

Q 6C-13-Q091medium

For a right circular cone of height $h$ , base radius $r$ , the slant height is which of the following?

a $h+r$
b $\sqrt{h^2-r^2}$
c $\sqrt{h^2+r^2}$
d $hr$

Q 7C-13-Q092medium

A right circular cone has height 12 cm and base diameter 10 cm. The slant height is which of the following?

a11 cm
b12 cm
c13 cm
d17 cm

Q 8C-13-Q093medium

A right circular cone has height 12 cm and base diameter 10 cm. The area of its curved surface is approximately which of the following?

a78.54 sq cm
b204.20 sq cm
c282.74 sq cm
d314.16 sq cm

Q 9C-13-Q094medium

A right circular cone has height 12 cm and base diameter 10 cm. The total surface area is approximately which of the following?

a204.20 sq cm
b282.74 sq cm
c314.16 sq cm
d408.41 sq cm

Q 10C-13-Q095medium

A right circular cone has height 12 cm and base diameter 10 cm. Its volume is approximately which of the following?

a204.20 cubic cm
b282.74 cubic cm
c314.16 cubic cm
d942.48 cubic cm

Q 11C-13-Q096medium

For a right circular cone of volume $V$ , slant height $l$ , base radius $r$ , height $h$ , semi-vertical angle $\alpha$ , which formula gives the curved surface area $S$ ?

a $S = \pi r^2$
b $S = \dfrac{\pi h^2 \tan\alpha}{\cos\alpha}$
c $S = \pi r h$
d $S = \dfrac{1}{3}\pi r^2 h$

Q 12C-13-Q097medium

For a right circular cone of base radius $r$ and semi-vertical angle $\alpha$ , the volume can be expressed as which of the following?

a $\dfrac{\pi r^3}{3 \tan\alpha}$
b $\pi r^3 \tan\alpha$
c $\dfrac{\pi r^2}{\sin\alpha}$
d $\dfrac{4}{3}\pi r^3$

14.Sphere7

Q 1C-13-Q098medium

A sphere is formed by a complete revolution of a semicircle about what?

aits radius
bits diameter as axis
cits tangent
dits chord

Q 2C-13-Q099medium

The surface area of a sphere of radius $r$ is which of the following?

a $\pi r^2$
b $2\pi r^2$
c $4\pi r^2$
d $\dfrac{4}{3}\pi r^2$

Q 3C-13-Q100medium

The volume of a sphere of radius $r$ is which of the following?

a $\pi r^3$
b $\dfrac{4}{3}\pi r^3$
c $\dfrac{1}{3}\pi r^3$
d $4\pi r^2$

Q 4C-13-Q101medium

A plane at a perpendicular distance $h$ from the centre of a sphere of radius $r$ cuts a circle of radius which of the following?

a $r-h$
b $\sqrt{r^2+h^2}$
c $\sqrt{r^2-h^2}$
d $r+h$

Q 5C-13-Q102medium

An iron sphere of diameter 4 cm is flattened into a circular sheet of thickness $\dfrac{2}{3}$ cm. The radius of the sheet is which of the following?

a2 cm
b3 cm
c4 cm
d6 cm

Q 6C-13-Q103medium

A right circular cone, a hemisphere and a cylinder of equal heights stand on equal bases. The ratio of their volumes is which of the following?

a1 : 2 : 3
b1 : 1 : 2
c2 : 3 : 4
d1 : 3 : 2

Q 7C-13-Q104medium

A rectangular iron block of dimensions $10, 8, 5\dfrac{1}{2}$ cm is melted into spherical shots of radius $\dfrac{1}{2}$ cm. The number of shots formed is approximately which of the following?

a660
b770
c840
d940

15.Compound solid8

Q 1C-13-Q105medium

A solid body consisting of two solids is called what?

acomposite shape
bcompound solid
chybrid solid
dmixed solid

Q 2C-13-Q106medium

A capsule is a compound solid having which of the following?

aa cylinder with a cone at one end
btwo cones joined at the base
ctwo identical hemispheres at two ends of a circular cylinder
da hemisphere on a square pyramid

Q 3C-13-Q107medium

A capsule has length 15 cm and radius 3 cm. The length of its cylindrical part is which of the following?

a6 cm
b9 cm
c12 cm
d15 cm

Q 4C-13-Q108medium

A capsule has length 15 cm and radius 3 cm. The total surface area is approximately which of the following?

a188.50 sq cm
b226.20 sq cm
c282.74 sq cm
d367.57 sq cm

Q 5C-13-Q109medium

A capsule has length 15 cm and radius 3 cm. The volume is approximately which of the following?

a282.74 cubic cm
b339.29 cubic cm
c367.57 cubic cm
d452.39 cubic cm

Q 6C-13-Q110medium

A hollow iron sphere has outer diameter 15 cm and thickness 2 cm. The volume of the hollow portion is approximately which of the following?

a523.60 cubic cm
b696.91 cubic cm
c1070.24 cubic cm
d1767.15 cubic cm

Q 7C-13-Q111medium

A hollow iron sphere has outer radius 7.5 cm and thickness 2 cm. A solid sphere is made from its iron. The radius of the solid sphere is approximately which of the following?

a5.50 cm
b6.35 cm
c7.50 cm
d9.00 cm

Q 8C-13-Q112medium

The solid sphere obtained from the iron of the hollow sphere (outer diameter 15 cm, thickness 2 cm) has surface area approximately which of the following?

a320.50 sq cm
b415.30 sq cm
c505.97 sq cm
d706.86 sq cm

16.Exercise 1329

Q 1C-13-Q113medium

A rectangular parallelepiped has length 16 m, breadth 12 m, height 4.5 m. Total surface area is which of the following?

a432 sq m
b540 sq m
c636 sq m
d768 sq m

Q 2C-13-Q114medium

A rectangular parallelepiped has length 16 m, breadth 12 m, height 4.5 m. Volume is which of the following?

a720 cubic m
b864 cubic m
c960 cubic m
d1080 cubic m

Q 3C-13-Q115medium

A rectangular parallelepiped has length 16 m, breadth 12 m, height 4.5 m. The diagonal length is which of the following?

a18.5 m
b20.0 m
c20.5 m
d22.0 m

Q 4C-13-Q116medium

A rectangular tank of length 2.5 m, breadth 1.0 m, height 0.4 m stands on the ground. Its volume is which of the following?

a0.5 cubic m
b1.0 cubic m
c1.5 cubic m
d2.0 cubic m

Q 5C-13-Q117medium

A rectangular tank of length 2.5 m, breadth 1.0 m, height 0.4 m has interior surface area (open top) of which of the following?

a4.5 sq m
b5.3 sq m
c6.0 sq m
d7.5 sq m

Q 6C-13-Q118medium

A hostel for 70 students provides each student 4.25 sq m floor area. If the room is 34 m long, the breadth is which of the following?

a7.50 m
b8.50 m
c8.75 m
d9.00 m

Q 7C-13-Q119medium

A hostel for 70 students provides each student 4.25 sq m floor and 13.6 cubic m of space, in a 34 m long room. The height is which of the following?

a2.8 m
b3.0 m
c3.2 m
d3.5 m

Q 8C-13-Q120medium

A right circular cone has height 24 cm and volume 1232 cubic cm. The slant height is which of the following?

a7 cm
b18 cm
c25 cm
d30 cm

Q 9C-13-Q121medium

A right-angled triangle has sides 5 cm and 3.5 cm. When revolved about its greater side, the volume of the solid formed is approximately which of the following?

a32.08 cubic cm
b64.17 cubic cm
c91.67 cubic cm
d192.50 cubic cm

Q 10C-13-Q122medium

Three glass balls of radii 6, 8 and $r$ cm are melted to form a single sphere of radius 9 cm. The value of $r$ is which of the following?

a1 cm
b2 cm
c3 cm
d5 cm

Q 11C-13-Q123medium

A hollow sphere has outer diameter 13 cm and iron thickness 2 cm. A solid sphere is made from its iron. Its diameter is approximately which of the following?

a9.0 cm
b10.5 cm
c11.4 cm
d12.5 cm

Q 12C-13-Q124medium

A solid sphere of radius 4 cm is melted to form a hollow sphere of outer radius 5 cm. The thickness of the second sphere is approximately which of the following?

a0.50 cm
b0.85 cm
c1.06 cm
d1.50 cm

Q 13C-13-Q125medium

A solid iron sphere has radius 6 cm. From its iron, how many solid cylinders of length 8 cm and diameter 6 cm can be formed?

Q 14C-13-Q126medium

A spherical ball of radius $\dfrac{22}{\pi}$ cm fits exactly into a cubical box. The volume of the unoccupied portion of the box is approximately which of the following?

a980.33 cubic cm
b1306.67 cubic cm
c1437.33 cubic cm
d2744.00 cubic cm

Q 15C-13-Q127medium

A sphere of radius 13 cm is cut by a plane perpendicular to a diameter through a point 12 cm from the centre. The area of the section formed is which of the following?

a $9\pi$ sq cm
b $16\pi$ sq cm
c $25\pi$ sq cm
d $36\pi$ sq cm

Q 16C-13-Q128medium

A wooden box with lid has outer dimensions $1.6 \times 1.2 \times 0.8$ m and wood thickness 3 cm. The area of the inner surface is approximately which of the following?

a6.50 sq m
b7.48 sq m
c8.40 sq m
d9.20 sq m

Q 17C-13-Q129medium

The wooden box of inner surface area approximately 7.48 sq m is to be painted at Tk 14.44 per sq m. The cost is approximately which of the following?

aTk 87.50
bTk 98.40
cTk 107.98
dTk 124.30

Q 18C-13-Q130medium

Bricks of size $25 \times 12.5 \times 8$ cm are used to build a wall of height 2 m and thickness 25 cm around a rectangular garden of length 120 m and width 90 m. Approximately how many bricks are required?

a42000
b67200
c84000
d96000

Q 19C-13-Q131medium

The length and breadth of a rectangular solid are in the ratio $4:3$ and its volume is 2304 cubic cm. The bottom lead-coating costs Tk 10 per sq cm and the total cost is Tk 1920. The dimensions are which of the following?

a $20 \times 15 \times 7.68$
b $16 \times 12 \times 12$
c $12 \times 9 \times 21.33$
d $24 \times 18 \times 5.33$

Q 20C-13-Q132medium

A regular hexagonal prism has side 4 cm and height 5 cm. The volume is approximately which of the following?

a120.00 cubic cm
b150.50 cubic cm
c207.85 cubic cm
d240.00 cubic cm

Q 21C-13-Q133medium

A regular hexagonal prism has side 4 cm and height 5 cm. The total surface area is approximately which of the following?

a120.00 sq cm
b167.85 sq cm
c203.14 sq cm
d240.00 sq cm

Q 22C-13-Q134medium

A pyramid has a regular hexagonal base of side 6 cm and height 10 cm. The volume is approximately which of the following?

a180.00 cubic cm
b311.77 cubic cm
c400.00 cubic cm
d540.00 cubic cm

Q 23C-13-Q135medium

A regular tetrahedron has edge 8 cm. Its total surface area is which of the following?

a $32\sqrt{3}$ sq cm
b $48\sqrt{3}$ sq cm
c $64\sqrt{3}$ sq cm
d $96\sqrt{3}$ sq cm

Q 24C-13-Q136medium

A regular tetrahedron has edge 8 cm. Its volume is approximately which of the following?

a30.17 cubic cm
b60.34 cubic cm
c90.50 cubic cm
d128.00 cubic cm

Q 25C-13-Q137medium

A construction has a square parallelepiped of base 2 m and height 3 m, with a regular pyramid of base edge 2 m and height 3 m on top. The total volume is which of the following?

a12 cubic m
b14 cubic m
c16 cubic m
d18 cubic m

Q 26C-13-Q138medium

A right circular conical tent has base diameter 50 m and height 8 m. Its slant height is approximately which of the following?

a22.50 m
b24.00 m
c26.25 m
d30.00 m

Q 27C-13-Q139medium

A right circular conical tent has base diameter 50 m and height 8 m. The land required (base area) is approximately which of the following?

a1257 sq m
b1571 sq m
c1964 sq m
d2375 sq m

Q 28C-13-Q140medium

A right circular conical tent has base diameter 50 m and height 8 m. The volume of vacuum space inside the tent is approximately which of the following?

a3142 cubic m
b5238 cubic m
c6283 cubic m
d7854 cubic m

Q 29C-13-Q141medium

A right circular conical tent has base diameter 50 m and height 8 m. The cost of canvas at Tk 125 per sq m is approximately which of the following?

aTk 154,820
bTk 198,750
cTk 257,813
dTk 314,159

17.Multiple Choice (Book)4

Q 1C-13-Q142medium

A rectangular parallelepiped's length is 5 cm, width 4 cm and height 3 cm. What's its diagonal?

a $5\sqrt{2}$ cm
b25 cm
c $25\sqrt{2}$ cm
d50 cm

Q 2C-13-Q143combomedium

Lengths of the other two sides except the hypotenuse of a right-angled triangle are 4 cm and 3 cm. If the triangle is revolved about the larger side:

the evolved solid will be a right circular cone
the evolved solid will be a right circular cylinder
the area of the base of the evolved solid is $9\pi$ square centimetres

ai
bii
ci & iii
dii & iii

Q 3C-13-Q144medium

A spherical ball of diameter 2 cm exactly fits in a cylindrical box. What is the volume of the cylinder?

a $2\pi$ cc
b $4\pi$ cc
c $6\pi$ cc
d $8\pi$ cc

Q 4C-13-Q145medium

A spherical ball of diameter 2 cm exactly fits in a cylindrical box. What is the volume of the unoccupied portion of the cylinder?

a $\dfrac{\pi}{3}$ cc
b $\dfrac{2\pi}{3}$ cc
c $\dfrac{4\pi}{3}$ cc
d $\dfrac{8\pi}{3}$ cc

18.Creative Questions3

Q 1C-13-Q146medium

A solid iron sphere has diameter 12 cm. The surface area of the sphere is which of the following?

a $36\pi$ sq cm
b $72\pi$ sq cm
c $144\pi$ sq cm
d $288\pi$ sq cm

Q 2C-13-Q147medium

A solid iron sphere of diameter 12 cm is melted into solid right circular cylinders of length 8 cm and diameter 6 cm. The number of cylinders formed is which of the following?

Q 3C-13-Q148medium

A solid iron sphere of diameter 12 cm fits perfectly into a cubic box. The volume of the unoccupied part of the box is approximately which of the following?

a432.00 cubic cm
b596.40 cubic cm
c823.22 cubic cm
d1024.00 cubic cm

19.Short Answer Questions4

Q 1C-13-Q149medium

The diagonal of a rectangular solid of dimensions $5, 4, 3$ cm equals the edge of a cube. The total surface area of the cube is which of the following?

a200 sq cm
b250 sq cm
c300 sq cm
d360 sq cm

Q 2C-13-Q150medium

A right circular cone has height 8 cm and base radius 6 cm. Its total surface area is which of the following?

a $36\pi$ sq cm
b $60\pi$ sq cm
c $96\pi$ sq cm
d $120\pi$ sq cm

Q 3C-13-Q151medium

A right circular cone has height 8 cm and base radius 6 cm. Its volume is which of the following?

a $48\pi$ cubic cm
b $96\pi$ cubic cm
c $144\pi$ cubic cm
d $288\pi$ cubic cm

Q 4C-13-Q152medium

A triangular prism has base sides 6, 8, 10 cm and height 12 cm. Its volume is which of the following?

a144 cubic cm
b240 cubic cm
c288 cubic cm
d480 cubic cm