MCQ Questions for Class 9 Maths Surface Areas And Volumes Quiz 1

The length of diagonal of a cube is

$15\sqrt { 2 }$ cm, then the length of its side is:

0%
$30\sqrt { 2 }$ cm
0%
15 cm
0%
$5\sqrt { 6 }$ cm
0%
30 cm

State whether the given statement is True or False.
One cubic meter is equal to one litre.

0%
True
0%
False

Explanation

We know one cubic meter is equal to

$1000$ liters.

Thus the given statement that one cubic metre is equal to one litre is false.

The volume of a solid is the measurement of the portion of the space occupied by it.

State True or False.

0%
True
0%
False
0%
Data Insufficient
0%
None of the above

Find the volume and surface area of a sphere of radius

$4.2$ cm.

$\displaystyle \left [ \pi =\frac{22}{7} \right ]$

0%
$380.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
0%
$320.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
0%
$310.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
0%
$370.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$

Explanation

Given, radius of sphere

$=4.2$ cm

Volume of sphere

$= \dfrac { 4 }{ 3 } \pi { r }^{ 3 }$

$= \dfrac {4}{3} \times \dfrac {22}{7} \times 4.2 \times 4.2 \times 4.2 = 310.46 \ \text{cm}^{3}$
Surface area of a sphere of radius '

$r$ '

$= 4\pi { r }^{ 2 } = 4 \times \dfrac {22}{7} \times 4.2 \times 4.2 = 221.76 \ \text{cm}^{2}$

Find the volume of a sphere whose radius is

$7\ cm$

0%
$1437\cfrac{1}{3}{cm}^{3}$
0%
$1437\cfrac{1}{4}{cm}^{3}$
0%
$1437\cfrac{2}{3}{cm}^{3}$
0%
$1437\cfrac{1}{2}{cm}^{3}$

Explanation

radius of sphere

$=7cm$
volume of sphere

$=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }=\cfrac { 4 }{ 3 } \times \cfrac { 22 }{ 7 } \times 7\times 7\times 7=\cfrac { 4312 }{ 3 } cm\\ =1437\cfrac { 1 }{ 3 } { cm }^{ 3 }$

The surface area of a cube of side is

$27\ \text{cm}$ is:

0%
$2916{\ \mathrm{cm}}^{2}$
0%
$729{\ \mathrm{cm}}^{2}$
0%
$4374{\ \mathrm{cm}}^{2}$
0%
$19683{\ \mathrm{cm}}^{2}$

Explanation

Surface area of a cube of side $a$ is given by, $S=6\ a^2$

The side of cube is given , $a=27\ \mathrm{cm}$

Total surface area of given cube of side $a = 6{a}^{2}=6\times 27^2\ \mathrm{cm}^2$
$= 4374\ \mathrm{cm}^{2}$

The volume of a sphere of diameter

$d$ is:

0%
$\dfrac {\pi d^3}{3}$
0%
$\dfrac {\pi d^3}{6}$
0%
$\dfrac {2\pi d^3}{3}$
0%
$\dfrac {\pi d^3}{4}$

Explanation

Volume of sphere

$=\cfrac 43(\pi)r^3=\cfrac 43(\pi)\left(\cfrac d2\right)^3 = \cfrac {\pi d^3}{6}$

Curved surface area of hemisphere of diameter

$2 r$ is :

0%
$2\pi r^{2}$
0%
$3\pi r^{2}$
0%
$4\pi r^{2}$
0%
$8\pi r^{2}$

Explanation

Diameter

$=2r$

Radius

$=r$

$\therefore$ Curved surface area of hemisphere

$=2\pi { r }^{ 2 }$

The ratio of the volumes of two spheres is

$8 : 27$ . The ratio of their radii is

0%
$3 : 2$
0%
$2 : 3$
0%
$4 : 3$
0%
$2 : 9$

Explanation

Given, ratio of volume of spheres

$= 8 : 27$
Volume of sphere

$= \displaystyle \frac{4}{3} \pi r^3$
Let

$R$ be the radius of one sphere and

$r$ be the radius of another sphere.

$\therefore$ Ratio

$=\dfrac{\frac{4}{3} \pi R^3}{\frac{4}{3} \pi r^3}$

$= 8:27$

$\therefore \dfrac{R^3}{r^3}$

$= 8:27$

$\therefore \dfrac{R}{r} = 2: 3$

Volume of a cuboid whose

$l=3.5$ m,

$b =2.5$ m and

$h =1.5$ m is

0%
$13.12$ cu m
0%
$13.215$ cu m
0%
$13.125$ cu m
0%
$13.521$ cu m

Explanation

Since, volume of cuboid

$=$ length

$\times$ breadth

$\times$ height

Here, length

$=$

$3.5$ m, breadth

$=$

$2.5$ m and height

$=$

$1.5$ m

$\therefore$ Volume of cuboid

$=$

$3.5\times 2.5\times 1.5 = 13.125 m^3$

The radius of the cylinder whose lateral surface area is

$704{cm}^{2}$ and height

$8$ cm is:

0%
$6$ cm
0%
$4$ cm
0%
$8$ cm
0%
$14$ cm

Explanation

Curved surface area of a cylinder of radius " $R$ " and height " $h$ " $= 2\pi Rh$
Hence, Curved surface area of the given cylinder $= 2\times \dfrac {22}{7} \times r \times 8 = 704$

$\therefore r = 14$ cm

Radius of the base of the cylinder is $14$ cm

The radius of a sphere of lead is

$8$ cm. The number of spheres of radius

$5$ mm made by melting it will be

0%
$6000$ approx
0%
Greater than $4000$ and less than $5000$
0%
Greater than $3000$ and less than $4000$
0%
Less than $3000$

Explanation

Number of spheres =

$\dfrac { volume\quad of\quad sphere\quad of\quad radius\quad 80mm\quad (8cm) }{ Volume\quad of\quad sphere\quad of\quad radius\quad 5\quad mm } \quad =\quad \dfrac { \dfrac { 4\pi }{ 3 } \quad *\quad { 80 }^{ 3 } }{ \dfrac { 4\pi }{ 3 } \quad *\quad { 5 }^{ 3 } } \quad =\quad \dfrac { 512000 }{ 125 } \quad =\quad 4096$
(Greater than

$4000$ and less than

$5000$ )

If radius of a sphere is doubled, how many times its volume will be affected?

0%
2 times
0%
4 times
0%
6 times
0%
8 times

Explanation

$\upsilon = \displaystyle \frac{4}{3} \pi r^3$
Now new radius:

$r' = 2r$
New volume:

$\upsilon' = \displaystyle \frac{4}{3} \pi (2r)^3$

$= 8 \displaystyle \left ( \frac{4}{3} \pi r^3 \right )$

$\upsilon' = 8 \upsilon$ .

If the curved surface area of a cylinder is

$1760$ sq.cm and its base radius is

$14$ cm, then its height is:

0%
$10$ cm
0%
$15$ cm
0%
$20$ cm
0%
$40$ cm

Explanation

Given, curved surface varea of cone $=1760$ sq.cm and radius $=14$ cm

Curved surface area of a cylinder of radius " $R$ " and height " $h$ " $= 2\pi Rh$

Hence, curved surface area of the given cylinder $= 2\times \dfrac {22}{7} \times 14\times h = 1760$ sq.cm

$\therefore h = 20$ cm

A reservoir is 3 m long, 2 m wide and 1 deep. Its capacity in litres is

0%
8000 litres
0%
10000 litres
0%
6500 litres
0%
6000 litres

Explanation

Volume of the reservoir = l x b x h=3 x 2 x 1=6 cu m

$\displaystyle \left ( \because 1 cu\, m = 1000 litre \right )$
(

$\displaystyle \because$ Capacity of the reservoir =6 x 1000 =6000 litre.

The number of surface areas in right circular cylinder is

0%
$1$
0%
$2$
0%
$3$
0%
$4$

Explanation

As shown in figure of right circular cylinder, we have

$3$ Surface areas they are :

Top Circular base area

$= \pi r^2$

Lateral Surface area

$=2 \pi r$

Bottom Circular base area

$=\pi r^2$

hence, option

$C$ is correct.

Find the volume of a sphere of radius

$2.1\;cm$ .

0%
$34.8\;cm^3$
0%
$35.8\;cm^3$
0%
$38.8\;cm^3$
0%
$36.8\;cm^3$

Explanation

Volume of sphere

$=$

$\dfrac { 4 }{ 3 } \pi { r }^{ 2 }=\dfrac { 4 }{ 3 } \times \dfrac { 22 }{ 7 } \times 2.1\times 2.1\times 21$

$=$

$38.8$

${ cm }^{ 3 }$

The diameter of a sphere is 21 cm. Calculate its volume

0%
4851 $\displaystyle cm^{3}$
0%
4000 $\displaystyle cm^{3}$
0%
2000 $\displaystyle cm^{3}$
0%
3850 $\displaystyle cm^{3}$

Explanation

Diameter = 21 cm

$\displaystyle r=\dfrac{21}{2}cm$
Volume of the sphere

$\displaystyle =\dfrac{4}{3}\pi r^{3}$

$\displaystyle =\dfrac{4}{3}\times \dfrac{22}{7}\times \dfrac{21}{2}\times \dfrac{21}{2}\times \dfrac{21}{2}$
$\displaystyle= 4851 cm^{3}$

The radius of a sphere is 3 cm. Its volume is:

0%
113.14 $\displaystyle cm^{3}$
0%
120 $\displaystyle cm^{3}$
0%
108 $\displaystyle cm^{3}$
0%
112.12 $\displaystyle cm^{3}$

Explanation

Volume of sphere

$\displaystyle =\dfrac{4}{3}\pi r^{3}$

$=\dfrac{4}{3}\times \dfrac{22}{7}\times \left ( 3 \right )^{3}$

$=113.14cm^{3}$

If the surface area of a sphere is

$\displaystyle 324\pi cm^{2}$ then its volume is

0%
$\displaystyle 950 \pi$ $\displaystyle cm^{3}$
0%
$\displaystyle 972 \pi$ $\displaystyle cm^{3}$
0%
$\displaystyle 975 \pi$ $\displaystyle cm^{3}$
0%
$\displaystyle 980\pi$ $\displaystyle cm^{3}$

Explanation

Given the surface area of sphere is

$324\pi cm^{2}$

$\therefore 4\pi r^{2}=324\pi \Rightarrow r^{2}=81\Rightarrow r=9$ cm

then volume of sphere=

$\frac{4}{3}\pi (9)^{3}=\frac{4}{3}\times \pi \times 729=972\pi cm^{3}$

If the volume in

$\displaystyle m ^{2}$ and the surface area in

$\displaystyle m ^{2}$ of a sphere are numerically equal then the radius of the sphere in m is

0%
4
0%
2
0%
3.5
0%
3

Explanation

Let the radius of the sphere is m

So volume of sphere=

$\frac{4}{3}\pi m^{3}$

And surface area of sphere=

$4\pi m^{2}$

As per question both are numerically equal

$\therefore \frac{4}{3}\pi m^{3}=\pi m^{2}\Rightarrow m=3$

$l \times b \times h$ is formula of---

0%
Area of cube
0%
Area of cuboid
0%
Volume of a cuboid
0%
None of these

The volume of a sphere of diameter 2p cm is given by

0%
$\displaystyle \pi p^{2}cm ^{3}$
0%
$\displaystyle \pi p^{3}cm ^{3}$
0%
$\displaystyle 4 \pi p^{2}cm ^{3}$
0%
$\displaystyle \frac{4}{3}\pi p^{3}cm ^{3}$

Explanation

GIven the diameter of sphere is 2p

Then radius of sphere=

$\frac{2p}{2}=p cm$

Then volume of sphere=

$\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi (p)^{3}=\frac{4}{3}\pi p^{3}cm^{3}$

If the radius of a sphere is doubled what is the ratio of the volume of the first sphere to that of the second?

0%
$2:8$
0%
$1:2$
0%
$1:3$
0%
$1:8$

Explanation

Let the radius be

$r$ If the radius is doubled the new radius will be

$2r$ Therefore
Ratio of volumes

$=\displaystyle \dfrac{4}{3}\pi r^{3}:\dfrac{4}{3}\pi \left ( 2r \right )^{3}$

$=\displaystyle r^{3}:8r^3$

$=\displaystyle 1:8$

2(lb + bh + hl) is formula of---

0%
Area of a cuboid
0%
Area of a cube
0%
Volume of a cuboid
0%
None of these

If the radius of a sphere is doubled then the volume of a sphere becomes

0%
doubled
0%
six times
0%
four times
0%
eight times

Explanation

Let the radius of sphere is r

Then volume of sphere =

$\frac{4}{3}\pi r^{3}$

If radius of sphere is doubled then radius is 2r

Then volume of new sphere =

$\frac{4}{3}\pi (2r)^{3}=\frac{4}{3}\times 8r^{3}$

Then ratio of new and old sphere=

$\frac{\frac{4}{3}\times 8r^{3}}{\frac{4}{3}r^{3}}=\frac{8}{1}$

Then the radius of sphere is doubled then volume become eight times

Find the volume of the sphere whose diameter is 30 cm.

0%
1.41428 cm $\displaystyle ^{3}$
0%
1414.28 cm $\displaystyle ^{3}$
0%
141.428 cm $\displaystyle ^{3}$
0%
14142.8 cm $\displaystyle ^{3}$

Explanation

Given: Diameter

$= 30 cm$

$\displaystyle \therefore Radius = \frac{30}{2}= 15 cm$

$\displaystyle \therefore\ Volume\ of\ the\ sphere =\frac{4}{3}\pi r^{3}=\frac{4}{3}\times \frac{22}{7}\times 15\times 15\times 15=14142.8 5cm^{3}$

The curved surface area of a hemisphere of diameter

$2 r$ is:

0%
$\displaystyle 2\pi r^{2}$
0%
$\displaystyle 3\pi r^{2}$
0%
$\displaystyle 4\pi r^{2}$
0%
$\displaystyle 8\pi r^{2}$

Explanation

Diameter of the hemisphere=

$2r$

$\therefore \text{Radius}=\dfrac{2r}{2}=r \ \text{cm}$

Curved surface area of hemisphere

$=2 \pi r^2$

The total surface area of a cube is ____ .

0%
$\displaystyle 3{ a }^{ 2 }$
0%
$\displaystyle 6{ a }^{ 2 }$
0%
$\displaystyle 4{ a }^{ 2 }$
0%
$\displaystyle 5{ a }^{ 2 }$

Explanation

A cube has all edges of the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face

$\displaystyle 6{ a }^{ 2 }$ where

$a$ is edge length of the cube.

Lateral surface area of a cylinder is

0%
$2\pi r^2$
0%
$2\pi rh^2$
0%
$2\pi rh$
0%
None

Explanation

Area of lateral surface of cylinder

$=$ Curved surface of cylinder

Curved surface of cylinder

$=$ Circumference of circular base

$\times$ height

Therefore, lateral surface area of a cylinder

$=2 \pi r h$

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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