Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

Fill in the blanks :
Curved surface area of a cylinder = ____

A
Circumference of a base $$\times$$ height

B
Area of a circle $$\times$$ radius

C
Circumference of a base $$\times$$ radius

D
Area of a circle $$\times$$ height

Solution

The curved surface area of a cylinder is the circumference of a base $$\times$$ height.
Question 2
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Which formula is used to calculate the curved surface area of a cylinder?

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

B
$$\displaystyle 2\pi rh$$

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

D
$$\displaystyle 2\pi r$$

Solution

Curved surface area of a cylinder is circumference of a base $\times$$ height.
Curved surface area of a cylinder $$=$$ $$\displaystyle 2\pi rh$$.
Question 3
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Find the volume of cuboid with length $$= 3a$$, brcadth $$= 7b$$ and height $$= c$$.

A
$$21a$$

B
$$21abc$$

C
$$21bc$$

D
$$21c$$

Solution

Volume of the cuboid = $$l \times b \times h$$ = $$3a\times 7b\times c$$
$$ = (3\times 7)\times a\times b\times c $$
$$= 21 abc$$
Question 4
1 / -0

Volume of a sphere is calculated by:

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

B
$$\displaystyle \frac { 4 }{ 3 } \pi { r }^{ 2 }$$

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

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

Solution

Volume of a sphere $$\displaystyle =\frac { 4 }{ 3 } \pi { r }^{ 3 }$$
Volume of a hemi-sphere $$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$$
Where, $$r$$ is the radius.
Question 5
1 / -0

Find the volume of a sphere, whose diameter is $$8\ mm$$.(Take $$\pi=3.14$$) (Round your answer to the nearest tenth).

A
$$\displaystyle 243.6{ mm }^{ 3 }$$

B
$$267.94\ mm^3$$

C
$$\displaystyle 1,143.6{ mm }^{ 3 }$$

D
$$\displaystyle 2,143.6mm$$

Solution

Formula:
Volume of sphere$$=\dfrac{4}{3}\pi r^3$$
where,
$$r=radius$$
Given:
$$r=4mm$$
After substituting the values in the formula we get:
$$ \dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times3.14\times4^3$$

$$=\dfrac{4}{3}\times3.14\times4\times4\times4$$

$$=\dfrac{803.84}{3}$$

$$=267.94\ mm^3$$
Question 6
1 / -0

Calculate the volume of a sphere with radius $$2\ m. (\pi = 3.142)$$

A
$$33.51\ m^3$$

B
$$73.51\ m^3$$

C
$$63.51\ m^3$$

D
None of these

Solution

Vol. of sphere $$V = \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\times 3.14 \times 2^{3} $$

$$V =\dfrac{4}{3}\times 3.14 \times 8 $$

$$=\dfrac{32}{3}\times 3.14 $$

$$=\dfrac{100.48}{3}=33.49\ m^3 $$
Question 7
1 / -0

Calculate the volume of a hemisphere with radius $$7$$ cm. $$\left ( \pi = \dfrac{22}{7} \right)$$

A
$$718.67$$ cm$$^3$$

B
$$78.67$$ cm$$^3$$

C
$$18.67$$ cm$$^3$$

D
None of these

Solution

Formula for volume of hemisphere $$ = \dfrac{2}{3}\pi r^{3}$$
Given, $$r=7\ cm $$
Volume:
$$V = \dfrac{2}{3}\times \dfrac{22}{7}\times 7^{3} \\ = \boxed {718.67\ cm^3} \ $$
Question 8
1 / -0

The surface area of a sphere is given by the formula:

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

B
$$\displaystyle 4\pi r$$

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

D
$$\displaystyle \dfrac {1}{2}\pi { r }^{ 2 }$$

Solution

We know that the surface area of a sphere is exactly four times the area of a circle with the same radius.
Also, area of circle $$=\pi r^2$$.
Then, area of sphere $$=4\times \pi r^2$$.
Therefore, the surface area of a sphere is given by the formula $$\displaystyle 4\pi { r }^{ 2 }$$.
Hence, option $$A$$ is correct.
Question 9
1 / -0

Calculate the surface area of a sphere of radius $$2.8$$ cm.

A
$$98.56$$ cm$$^2$$

B
$$68.56$$ cm$$^2$$

C
$$38.56$$ cm$$^2$$

D
None of these

Solution

Given, radius $$r=2.8$$ cm.

We know that, the surface area of a sphere of radius $$r$$ $$= 4\pi { r }^{ 2 } $$

$$= 4 \times \dfrac {22}{7} \times 2.8 \times 2.8 $$

$$= 98.56 {cm}^{2} $$.
Therefore, option $$A$$ is correct.
Question 10
1 / -0

Calculate the surface area of sphere.

A
$$\displaystyle 5,024\ cm$$

B
$$\displaystyle 314{\ cm }^{ 2 }$$

C
$$\displaystyle 5,024{\ m }^{ 2 }$$

D
$$\displaystyle 5,024{ \ mm }^{ 2 }$$

Solution

We know, surface area of sphere, $$A=4\pi r^2$$.
Given, diameter, $$d=10\ cm$$.
Then, radius, $$r=\dfrac{d}{2}=\dfrac{10}{2}=5\ cm$$.
After substituting the values in the formula we get:
Surface area of the sphere,
$$A=4\times3.14\times5^2$$
$$=4\times3.14\times5\times5$$
$$=314\ cm^2$$.
Therefore, option $$B$$ is correct.

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 20

Result

Surface Areas and Volumes Test - 20

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SHARING IS CARING

Question 1

Circumference of a base $$\times$$ height

Area of a circle $$\times$$ radius

Circumference of a base $$\times$$ radius

Area of a circle $$\times$$ height

Solution

Question 2

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

$$\displaystyle 2\pi rh$$

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

$$\displaystyle 2\pi r$$

Solution

Question 3

$$21a$$

$$21abc$$

$$21bc$$

$$21c$$

Solution

Question 4

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

$$\displaystyle \frac { 4 }{ 3 } \pi { r }^{ 2 }$$

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

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

Solution

Question 5

$$\displaystyle 243.6{ mm }^{ 3 }$$

$$267.94\ mm^3$$

$$\displaystyle 1,143.6{ mm }^{ 3 }$$

$$\displaystyle 2,143.6mm$$

Solution

Question 6

$$33.51\ m^3$$

$$73.51\ m^3$$

$$63.51\ m^3$$

None of these

Solution

Question 7

$$718.67$$ cm$$^3$$

$$78.67$$ cm$$^3$$

$$18.67$$ cm$$^3$$

None of these

Solution

Question 8

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

$$\displaystyle 4\pi r$$

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

$$\displaystyle \dfrac {1}{2}\pi { r }^{ 2 }$$

Solution

Question 9

$$98.56$$ cm$$^2$$

$$68.56$$ cm$$^2$$

$$38.56$$ cm$$^2$$

None of these

Solution

Question 10

$$\displaystyle 5,024\ cm$$

$$\displaystyle 314{\ cm }^{ 2 }$$

$$\displaystyle 5,024{\ m }^{ 2 }$$

$$\displaystyle 5,024{ \ mm }^{ 2 }$$

Solution

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