Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 40

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Find the surface area of a sphere.

A
$$\displaystyle 452.16{ ft }^{ 2 }$$

B
$$\displaystyle 455.16 ft$$

C
$$\displaystyle 452.16{ \ cm }^{ 2 }$$

D
$$\displaystyle 455.16{ \ m }^{ 2 }$$

Solution

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.
Question 2
1 / -0

The radius of the given figure below is $$21$$ mi. Find its volume. (use $$\displaystyle \pi =\frac { 22 }{ 7 } $$).

A
$$\displaystyle 19,504{\ mi }^{ 3 }$$

B
$$\displaystyle 19,404\ mi$$

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

D
$$\displaystyle 29,504{ \ mi }^{ 3 }$$

Solution

Radius of the given figure is $$21$$ mi
Volume of hemisphere $$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$$
$$\displaystyle =\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times 21\times 21\times 21$$
$$\displaystyle =19,404{\ mi }^{ 3 }$$
Question 3
1 / -0

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

A
$$\displaystyle 30.493{ cm }^{ 3 }$$

B
$$\displaystyle 13.493{ cm }^{ 3 }$$

C
$$\displaystyle 23.493{ cm }^{ 3 }$$

D
$$\displaystyle 33.493{ cm }^{ 3 }$$

Solution

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:
$$\Rightarrow \dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times3.14\times2^3$$
$$=\dfrac{4}{3}\times3.14\times2\times2\times2$$
$$=\dfrac{4}{3}\times3.14\times8$$
$$=\dfrac{100.48}{3}$$
$$=33.493\ cm^3$$
Question 4
1 / -0

What is the surface area of the given sphere?

A
$$\displaystyle 9256{ \ in }^{ 2 }$$

B
$$\displaystyle 9756{\ in }^{ 2 }$$

C
$$\displaystyle 615.44{ \ in }^{ 2 }$$

D
$$\displaystyle 9856\ in$$

Solution

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.
Question 5
1 / -0

What is the volume of the hemisphere with a diameter $$5.5$$ in. ?

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

B
$$\displaystyle 2786.22\ in$$

C
$$\displaystyle 86.22{\ in }^{ 3 }$$

D
$$\displaystyle 2686.22{\ in }^{ 3 }$$

Solution

$$\displaystyle Diameter=\frac { radius }{ 2 } $$
$$\displaystyle 5.5\times 2=radius$$
$$\displaystyle Radius=11in$$
Volume of hemisphere $$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$$
$$\displaystyle =\frac { 2 }{ 3 } \times 3.14\times 11\times 11\times 11$$
$$\displaystyle 2786.22 {\ in }^{ 3 }$$
Question 6
1 / -0

Calculate the volume of the hemisphere with radius $$\dfrac {1}{3}$$ m.

A
$$\displaystyle 0.1325{ m }^{ 3 }$$

B
$$\displaystyle 0.2325{ cm }^{ 3 }$$

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

D
$$\displaystyle 0.325{ mm }^{ 3 }$$

Solution

Given, radius of hemisphere $$\dfrac {1}{3}$$ m
Volume of hemisphere $$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$$
$$\displaystyle =\frac { 2 }{ 3 } \times 3.14\times \frac { 1 }{ 3 } \times \frac { 1 }{ 3 } \times \frac { 1 }{ 3 } $$
$$\displaystyle =0.077{ m }^{ 3 }$$
Question 7
1 / -0

The surface area of a football is $$616{\ mm }^{ 2 }.$$ Calculate its radius.

A
$$4\ mm$$

B
$$7\ mm$$

C
$$6\ mm$$

D
$$5\ mm$$

Solution

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.
Question 8
1 / -0

A company packages its juice in a tetra pack shown below. How much quantity of juice does it contain.

A
$$\displaystyle 140{ cm }^{ 3 }$$

B
$$\displaystyle 160{ cm }^{ 3 }$$

C
$$\displaystyle 16{ cm }^{ 3 }$$

D
$$\displaystyle 136cm^3$$

Solution

Quantity of juice in the package $$=$$ Volume of cuboidal package
$$ =$$ $$l\times b\times h$$
$$=$$ $$4\times 4\times 10$$
$$=$$ $$160$$ $${ cm }^{ 3 }$$
Question 9
1 / -0

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

A
$$12$$ cm

B
$$10$$ cm

C
$$11$$ cm

D
$$9$$ cm

Solution

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
Question 10
1 / -0

The formula used for volume of the hemisphere is ______.

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

B
$$\displaystyle \frac { 1 }{ 3 } \pi { r }^{ 3 }$$

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

D
$$\displaystyle \frac { 5 }{ 3 } \pi { r }^{ 3 }$$

Solution

The formula used for volume of the hemisphere is $$\displaystyle \frac { 2 }{ 3 } \pi { r }^{ 3 }$$.