MCQ Questions for Class 9 Maths Surface Areas And Volumes Quiz 8

Calculate the volume of a sphere whose radius is

$3 \text{ cm}$ .

0%
$36\pi { \text{ cm} }^{ 3 }$
0%
$56\pi \text{ cm}^3$
0%
$36\pi { \text{ cm} }^{ 3 }$
0%
$46\pi {\text{ cm} }^{ 3 }$

Explanation

Formula: Volume of sphere =

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

Where,

$r=radius$

Given:

$r=3\text{ cm}$

Substitute the value of

$r$ in the above formula,

$\dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times3.14\times3^3$

$=\dfrac{4}{3}\times3\times3\times3\times \pi$

$=\dfrac{4}{3}\times27\times\pi$

$=\dfrac{108}{3}\times\pi$

$=36\pi\text{ cm}^3$

What is the volume of a sphere given: (Use

$\displaystyle \pi =3.14$ )

0%
$\displaystyle 1,13,140{\ m }^{ 3 }$
0%
$\displaystyle 1,13,040{\ m }^{ 3 }$
0%
$\displaystyle 1,03,040{\ m }^{ 3 }$
0%
$\displaystyle 2,13,040{\ m }^{ 3 }$

Explanation

Using formula for volume of sphere =

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

$r=radius$

Given:

$radius(r)=30\ m$

$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3} \times 3.14 \times 30^3$

$=\dfrac{4}{3} \times 30 \times 30 \times 30 \times 3.14$

$=\dfrac{4}{3} \times 27000 \times 3.14$

$=\dfrac{339120}{3}$

$=113040\ m^3$

The volume of sphere is

$\displaystyle 904.77{ cm }^{ 3 }$ . Find its radius. (Round off your answer to the nearest whole number).

0%
$2$ cm
0%
$5$ cm
0%
$6$ cm
0%
$7$ cm

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$volume=904.77\ cm^3$

After substituting the values in the formula we gte:

$904.77= \dfrac{4}{3}\pi r^3$

$\Rightarrow 904.77= \dfrac{4}{3}\times3.14\times r^3$

$\Rightarrow \dfrac{904.77\times3}{4\times3.14}=r^3$

$\Rightarrow r^3=\dfrac{2714.31}{12.56}$

$\Rightarrow r^3=215.42 \approx 216$

$\Rightarrow r=\sqrt[3]{216}$

$\Rightarrow r=6\ cm$

Calculate the volume of a sphere whose radius is

$12$ m.

0%
$\displaystyle 7134.56{\ m }^{ 3 }$
0%
$\displaystyle 7234.56{\ m }^{ 3 }$
0%
$\displaystyle 7034.56{ \ m }^{ 3 }$
0%
$\displaystyle 7334.56{ \ m }^{ 3 }$

Explanation

Formula:

Volume of sphere =

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

$r=radius$

Given:

$r=12\ m$

$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}*3.14*12^3$

$=\dfrac{4}{3}*12*12*12* 3.14$

$=\dfrac{4}{3}*1728*3.14$

$=\dfrac{21703.68}{3}$

$=7234.56\ m^3$

What is the diameter of the spherical ball whose volume is

$\displaystyle 268.08{ mm }^{ 3 }$ . (use

$\displaystyle \pi =3.14$ ). Round off your answer to nearest whole number.

0%
$4$ mm
0%
$3$ mm
0%
$1$ mm
0%
$8$ mm

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$volume=268.08 mm^3$

Substituting the values in the given formula we get:

$268.08= \dfrac{4}{3}\pi r^3$

$\Rightarrow 268.08= \dfrac{4}{3}\times3.14\times r^3$

$\Rightarrow \dfrac{268.08\times3}{4\times 3.14}=r^3$

$\Rightarrow r^3=\dfrac{804.28}{12.56}$

$\Rightarrow r^3=64.03 \approx 64$

$\Rightarrow r=\sqrt[3]{64}$

$\Rightarrow r=4\ mm$

Thus, the diameter

$=2r=8\ mm$ .

Find the volume of a sphere whose diameter is

$10$ in.

0%
$\displaystyle 523.33\ in$
0%
$\displaystyle 503.33{\ in }^{ 3 }$
0%
$\displaystyle 423.33{\ in }^{ 3 }$
0%
$\displaystyle 523.33{\ in }^{ 3 }$

Explanation

Formula:

Volume of sphere =

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

$r=radius$

Given:

$diameter(d)=10\ in$

$radius(r)=\dfrac{d}{2}=\dfrac{10}{2}=5\ in$

$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}*3.14*5^3$

$=\dfrac{4}{3}*5*5*5*3.14$

$=\dfrac{4}{3}*125*3.14$

$=\dfrac{1570}{3}$

$=523.33\ in^3$

The volume of a sphere is

$\displaystyle 300\pi { cm }^{ 3 }$ . Find its radius.

0%
$3.313$ cm
0%
$6.313$ cm
0%
$6.08$ cm
0%
$4.313$ cm

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$volume=300\pi cm^3$

After sustituting the values in the formula we get:

$300\pi= \dfrac{4}{3}\pi r^3$

$\Rightarrow 300= \dfrac{4}{3} r^3$ (

$\pi$ gets cancelled from both the sides)

$\Rightarrow \dfrac{300*3}{4}= r^3$

$\Rightarrow r^3=\dfrac{900}{4}$

$\Rightarrow r^3=225$

$\Rightarrow r=\sqrt[3]{225}$

$\Rightarrow r=6.08\ cm$

Find the surface area of a cylinder with the following dimension:
Height

$= 10$ ft.
Radius

$= 2$ ft.

0%
$\displaystyle 82\pi { ft }^{ 2 }$
0%
$\displaystyle 78\pi { ft }^{ 2 }$
0%
$\displaystyle 48\pi { ft }^{ 2 }$
0%
$\displaystyle 81\pi { ft }^{ 2 }$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here, radius is

$r=2$ ft and the height is

$h=10$ ft.

Thus,

$A=2π\times 2(2+10)=2π\times 2\times 12=48π$

Hence, the surface area of the cylinder is

$48π$ ft

$^2$ .

The volume of a sphere is

$\displaystyle 4000\pi { m }^{ 3 }$ . Find its surface area. (use

$\displaystyle \pi =\pi$ .)

0%
$\displaystyle 831.7456{ \ m }^{ 2 }$
0%
$\displaystyle2611.68{ \ m }^{ 2 }$
0%
$\displaystyle 631.7456{ \ m }^{ 2 }$
0%
$\displaystyle 801.7456{\ m }^{ 2 }$

Explanation

Volume of sphere

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

$\Rightarrow \displaystyle 4000\pi =\frac { 4 }{ 3 } \times \pi \times { r }^{ 3 }$

$\Rightarrow \displaystyle \dfrac {{ 4000\times 3 }}{{ 4 }}={ r }^{ 3 }$

$\Rightarrow \displaystyle \dfrac {12000}{4}={ r }^{ 3 }$

$\Rightarrow \displaystyle { r }^{ 3 }=3000$

$\Rightarrow \displaystyle r=\sqrt [ 3 ]{ 3000 }$

$\Rightarrow \displaystyle r=14.42$
Surface area of sphere

$\displaystyle =4\pi { r }^{ 2 }$

$\displaystyle =4\times \pi \times 14.42\times 14.42$

$\displaystyle =2611.68{ m }^{ 2 }$

Find the volume of a hemisphere whose radius is

$7$ cm. (use

$\displaystyle \pi =\frac { 22 }{ 7 }$ )

0%
$\displaystyle 112.66{ \ cm }^{ 3 }$
0%
$\displaystyle 718.66{\ cm }^{ 3 }$
0%
$\displaystyle 12.66{ \ cm }^{ 3 }$
0%
$\displaystyle 132.66{ \ cm }^{ 3 }$

Explanation

Given, radius of hemisphere

$=7$ cm

Volume of hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle =\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times 7\times 7\times 7$

$\displaystyle =718.66{ cm }^{ 3 }$

Calculate the surface area and volume of the sphere with diameter

$0.8$ in (use

$\displaystyle \pi =3$ ).

0%
$\displaystyle V=0.156{\ in }^{ 3 }$ and $A=1.92{\ in }^{ 2 }$
0%
$\displaystyle V=0.256{\ in }^{ 3 }$ and $A=0.92{\ in }^{ 2 }$
0%
$\displaystyle V=0.256{\ in }^{ 3 }$ and $A=1.92{ \ in }^{ 2 }$
0%
$\displaystyle V=0.156\ { in }^{ 3 }$ and $A=2.92{\ in }^{ 2 }$

Explanation

$\displaystyle \therefore$ radius

$=0.4$
Volume of sphere

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

$\displaystyle =\frac { 4 }{ 3 } \times 3\times 0.4\times 0.4\times 0.4$

$\displaystyle =0.256{ in }^{ 3 }$
Surface area of a sphere

$\displaystyle =4\pi { r }^{ 2 }$

$\displaystyle =4\times 3\times 0.4\times .4$

$\displaystyle =1.92{\ in }^{ 2 }$

Find the surface area of a sphere.

0%
$\displaystyle 452.16{ ft }^{ 2 }$
0%
$\displaystyle 455.16 ft$
0%
$\displaystyle 452.16{ \ cm }^{ 2 }$
0%
$\displaystyle 455.16{ \ m }^{ 2 }$

Explanation

We know, surface area of sphere,

$A=4\pi r^2$ .

Given, radius,

$r=6\ ft$ .

After substituting the value in the formula we get:

Surface area of the sphere,

$A=4\times3.14\times6^2$

$=4\times3.14\times6\times6$

$=452.16\ ft^2$ .

Therefore, option

$A$ is correct.

A spherical shape jar has a radius of 2 cm. What is the volume of the jar?

0%
$\displaystyle 30.493{ cm }^{ 3 }$
0%
$\displaystyle 13.493{ cm }^{ 3 }$
0%
$\displaystyle 23.493{ cm }^{ 3 }$
0%
$\displaystyle 33.493{ cm }^{ 3 }$

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$r=2\ cm$

After substituting the value sin the formula we get:

$\Rightarrow \dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times3.14\times2^3$

$=\dfrac{4}{3}\times3.14\times2\times2\times2$

$=\dfrac{4}{3}\times3.14\times8$

$=\dfrac{100.48}{3}$

$=33.493\ cm^3$

The volume of a sphere is

$\displaystyle 1150.35{ in }^{ 3 }$ . Find its radius. (Round off your answer to the nearest whole number).

0%
$2$ in
0%
$5$ in
0%
$8$ in
0%
$7$ in

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$volume=1150.35\ in^3$

After substituting the values in the formula we get:

$1150.35= \dfrac{4}{3}\pi r^3$

$\Rightarrow 1150.35= \dfrac{4}{3}*3.14* r^3$

$\Rightarrow \dfrac{1150.35*3}{4*3.14}=r^3$

$\Rightarrow r^3=\dfrac{3451.05}{12.56}$

$\Rightarrow r^3=274.76$

$\Rightarrow r=\sqrt[3]{274.76}$

$\Rightarrow r=6.50\approx 7\ in$

What is the surface area of the given sphere?

0%
$\displaystyle 9256{ \ in }^{ 2 }$
0%
$\displaystyle 9756{\ in }^{ 2 }$
0%
$\displaystyle 615.44{ \ in }^{ 2 }$
0%
$\displaystyle 9856\ in$

Explanation

We know, the surface area of sphere

$=4\pi r^2$ .

Given, diameter,

$d=14\ in$

Then, radius,

$r=\dfrac{d}{2}=\dfrac{14}{2}=7\ in$ .

After substituting the values in the given formula we get:

Surface area,

$A=4\times3.14\times7^2$

$=4\times3.14\times7\times7$

$=615.44\ in^2$ .

Therefore, option

$C$ is correct.

What is the volume of the hemisphere with a diameter

$5.5$ in. ?

0%
$\displaystyle 2786.22{ in }^{ 3 }$
0%
$\displaystyle 2786.22\ in$
0%
$\displaystyle 86.22{\ in }^{ 3 }$
0%
$\displaystyle 2686.22{\ in }^{ 3 }$

Explanation

$\displaystyle Diameter=\frac { radius }{ 2 }$

$\displaystyle 5.5\times 2=radius$

$\displaystyle Radius=11in$
Volume of hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle =\frac { 2 }{ 3 } \times 3.14\times 11\times 11\times 11$

$\displaystyle 2786.22 {\ in }^{ 3 }$

Calculate the volume of the hemisphere with radius

$\dfrac {1}{3}$ m.

0%
$\displaystyle 0.1325{ m }^{ 3 }$
0%
$\displaystyle 0.2325{ cm }^{ 3 }$
0%
$\displaystyle 0.077{ m }^{ 3 }$
0%
$\displaystyle 0.325{ mm }^{ 3 }$

Explanation

Given, radius of hemisphere

$\dfrac {1}{3}$ m

Volume of hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle =\frac { 2 }{ 3 } \times 3.14\times \frac { 1 }{ 3 } \times \frac { 1 }{ 3 } \times \frac { 1 }{ 3 }$

$\displaystyle =0.077{ m }^{ 3 }$

A swimming pool is

$200$ ft long and

$14$ ft wide and its depth being

$20$ ft respectively. Find the volume of the pool.

0%
$55,000 ft^{3}$
0%
$54,000 ft^{3}$
0%
$56,000 ft^{3}$
0%
$57,000 ft^{3}$

Explanation

Volume of the pool

$= l \times b \times h$

$= 200 \times 14 \times 20$

$= 56,000 ft^{3}$

The surface area of a football is

$616{\ mm }^{ 2 }.$ Calculate its radius.

0%
$4\ mm$
0%
$7\ mm$
0%
$6\ mm$
0%
$5\ mm$

Explanation

Let the radius of the football be

$r.$ then its surface area will be

$4\pi r^2.$

But it is given that, the surface area of football is equal to

$616\ mm^2.$

Hence,

$616=4 \pi r^2$

$\Rightarrow \displaystyle 616=4\times \frac { 22 }{ 7 } \times { r }^{ 2 }$

$\Rightarrow \displaystyle \dfrac {{ \left( 616\times 7 \right) }}{{ \left( 4\times 22 \right) }}={ r }^{ 2 }$

$\Rightarrow \displaystyle \dfrac {4312}{88}={ r }^{ 2 }$

$\Rightarrow \displaystyle 49={ r }^{ 2 }$

$\Rightarrow \displaystyle r=7\ mm$

Therefore, option

$B$ is correct.

The volume of the hemisphere is

$\displaystyle 2100{ cm }^{ 3 }$ . Find its radius. (Round off your answer to the nearest whole number).

0%
$12$ cm
0%
$10$ cm
0%
$11$ cm
0%
$9$ cm

Explanation

Volume of hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\Rightarrow \displaystyle 2100=\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times { r }^{ 3 }$

$\Rightarrow \displaystyle 2100\times 3\times \dfrac {7}{( 2\times 22)} ={ r }^{ 3 }$

$\Rightarrow \displaystyle \dfrac {44100}{44}={ r }^{ 3 }$

$\Rightarrow \displaystyle { r }^{ 3 }=1002.27$

$\Rightarrow \displaystyle r=\sqrt [ 3 ]{ 1002.27 }$

$\Rightarrow \displaystyle r=10$ cm

The radius of the given figure below is

$21$ mi. Find its volume. (use

$\displaystyle \pi =\frac { 22 }{ 7 }$ ).

0%
$\displaystyle 19,504{\ mi }^{ 3 }$
0%
$\displaystyle 19,404\ mi$
0%
$\displaystyle 19,404{\ mi }^{ 3 }$
0%
$\displaystyle 29,504{ \ mi }^{ 3 }$

Explanation

Radius of the given figure is

$21$ mi

Volume of hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle =\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times 21\times 21\times 21$

$\displaystyle =19,404{\ mi }^{ 3 }$

The formula used for volume of the hemisphere is ______.

0%
$\displaystyle \frac { 2 }{ 3 } \pi { r }^{ 3 }$
0%
$\displaystyle \frac { 1 }{ 3 } \pi { r }^{ 3 }$
0%
$\displaystyle \frac { 2 }{ 3 } \pi r$
0%
$\displaystyle \frac { 5 }{ 3 } \pi { r }^{ 3 }$

Explanation

The formula used for volume of the hemisphere is

$\displaystyle \frac { 2 }{ 3 } \pi { r }^{ 3 }$ .

If radius of sphere is doubled, what is the ratio of volume of original sphere to that of second?

0%
$1 : 4$
0%
$8 : 1$
0%
$1 : 8$
0%
None

Explanation

Given, radius of a sphere is doubled, i.e.

$\displaystyle r=2r$

Volume of sphere

$\displaystyle =\frac { 4 }{ 3 } \pi { r }^{ 3 }$ (original)
Vol of new sphere

$\displaystyle =\frac { 4 }{ 3 } \pi { \left( 2r \right) }^{ 3 }=\frac { 4 }{ 3 } \pi { \left( 8 \right) r }^{ 3 }$
Volume of original sphere / vol. of second sphere

$\displaystyle =\frac { { 4 }/{ 3 }\pi { r }^{ 3 } }{ { 4 }/{ 3 }\pi { r }^{ 3 }\left( 8 \right) } =\frac { 1 }{ 8 }$

Fill in the blank:

____________ is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.

0%
Mass
0%
Volume
0%
Capacity
0%
Density

The volume of the global hemisphere is

$\displaystyle 19404{ \ in }^{ 3 }$ . Find its diameter.

0%
$21$ in
0%
$42$ in
0%
$10.5$ in
0%
$9$ in

Explanation

Volume of the hemisphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle 19404=\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times { r }^{ 3 }$

$\displaystyle 19404\times 3\times \dfrac {7}{( 2\times 22 )} ={ r }^{ 3 }$

$\displaystyle \dfrac {407484}{44}={ r }^{ 3 }$

$\displaystyle { r }^{ 3 }=9261$

$\displaystyle r=\sqrt [ 3 ]{ 9261 }$

$\displaystyle r=21$ in
Diameter

$= 2 \times$ radius
Diameter

$=2 \times 21$
Diameter

$=$

$42$ in

The area of the hemisphere is

$\displaystyle 100{ m }^{ 2 }$ . Find its volume. (use

$\displaystyle \pi =3.14$ ).

0%
$\displaystyle 132.97{ m }^{ 3 }$
0%
$\displaystyle 102.97{ m }^{ 3 }$
0%
$\displaystyle 132.97m$
0%
$\displaystyle 132.97{ cm }^{ 3 }$

Explanation

Area of hemisphere

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

$\Rightarrow \displaystyle 100=2\times 3.14\times { r }^{ 2 }$

$\Rightarrow \displaystyle \dfrac {100}{( 2\times 3.14 ) }={ r }^{ 2 }$

$\Rightarrow \displaystyle R=\sqrt { 15.923 }$

$\Rightarrow \displaystyle R=3.99$ m
Volume of the hemisphere

$=$

$\displaystyle \frac { 2 }{ 3 } \pi { r }^{ 3 }$

$\displaystyle =\frac { 2 }{ 3 } \times 3.14\times 3.99\times 3.99\times 3.99$

$\displaystyle =132.97{ m }^{ 3 }$

Fill in the blank: The volume of solid objects is measured in _____ units.

0%
Cubic
0%
Square
0%
Meter
0%
Liter

It cost Rs

$4020$ to paint the inner curved surface area of hemisphere of radius

$8 m$ . If it is painted at rate of Rs.

$10\: per\: m^2$ . Find inner curved surface.

0%
$\displaystyle 402{ m }^{ 2 }$
0%
$\displaystyle 400{ m }^{ 2 }$
0%
$\displaystyle 200{ m }^{ 2 }$
0%
$\displaystyle 201{ m }^{ 2 }$

Explanation

CSA of hemisphere

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

$\displaystyle =2\pi { \left( 8 \right) }^{ 2 }=2\pi \times 64=402$

If lateral surface area of a cylinder of height 10 cm is 100 cm

$^{ 2 }$ , find radius of its base.

0%
$\displaystyle 5\pi$
0%
$\displaystyle \frac {5}{\pi}$
0%
$\displaystyle 6\pi$
0%
$\displaystyle \frac { \pi }{ 5 }$

Explanation

Given that, the lateral surface area of a cylinder of height

$10\ cm$ is

$100\ cm^2$ .

To find out: The radius of the base of the cylinder.

We know that, lateral surface area of a cylinder is

$\displaystyle 2\pi rh$

$\therefore \ 2\pi rh=100\\$

$\Rightarrow 2\pi r (10)=100\\$

$\Rightarrow 20\pi r =100\\$

$\Rightarrow r =\dfrac{100}{20\pi}\\$

$\therefore \ \displaystyle r=\dfrac { 5 }{ \pi }$

Hence, the radius of the base of the given cylinder is

$\dfrac { 5 }{ \pi }$ .

A swimming pool is 100 m long and 15 m wide its deep and 24 m height respectively. Find the capacity of the pool.

0%
36,000 m
0%
36,000 $m^3$
0%
36,000 $m^2$
0%
36,000 $cm$

Explanation

Volume of the pool =

$l \times b \times h$
=

$100 \times 15 \times 24$
=

$36000 m^3$

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 8 - 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 8 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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