Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 39

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Weekly Quiz Competition

Question 1
1 / -0

Calculate the volume of a sphere whose radius is $$3 \text{ cm}$$.

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

B
$$56\pi \text{ cm}^3$$

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

D
$$46\pi {\text{ cm} }^{ 3 }$$

Solution

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,
$$\dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times3.14\times3^3$$
$$=\dfrac{4}{3}\times3\times3\times3\times \pi$$
$$=\dfrac{4}{3}\times27\times\pi$$
$$=\dfrac{108}{3}\times\pi$$
$$=36\pi\text{ cm}^3$$
Question 2
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What is the volume of a sphere given: (Use $$\displaystyle \pi =3.14$$)

A
$$\displaystyle 1,13,140{\ m }^{ 3 }$$

B
$$\displaystyle 1,13,040{\ m }^{ 3 }$$

C
$$\displaystyle 1,03,040{\ m }^{ 3 }$$

D
$$\displaystyle 2,13,040{\ m }^{ 3 }$$

Solution

Using formula for volume of sphere =$$\dfrac{4}{3} \pi r^3$$
$$r=radius$$
Given: $$radius(r)=30\ m$$
$$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3} \times 3.14 \times 30^3$$
$$=\dfrac{4}{3} \times 30 \times 30 \times 30 \times 3.14$$
$$=\dfrac{4}{3} \times 27000 \times 3.14$$
$$=\dfrac{339120}{3}$$
$$=113040\ m^3$$
Question 3
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The volume of sphere is $$\displaystyle 904.77{ cm }^{ 3 }$$. Find its radius. (Round off your answer to the nearest whole number).

A
$$2$$ cm

B
$$5$$ cm

C
$$6$$ cm

D
$$7 $$ cm

Solution

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

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

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

$$\Rightarrow r^3=\dfrac{2714.31}{12.56}$$
$$\Rightarrow r^3=215.42 \approx 216$$
$$\Rightarrow r=\sqrt[3]{216}$$
$$\Rightarrow r=6\ cm$$
Question 4
1 / -0

Calculate the volume of a sphere whose radius is $$12$$ m.

A
$$\displaystyle 7134.56{\ m }^{ 3 }$$

B
$$\displaystyle 7234.56{\ m }^{ 3 }$$

C
$$\displaystyle 7034.56{ \ m }^{ 3 }$$

D
$$\displaystyle 7334.56{ \ m }^{ 3 }$$

Solution

Formula:
Volume of sphere =$$\dfrac{4}{3} \pi r^3$$
$$r=radius$$
Given:
$$r=12\ m$$
$$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}*3.14*12^3$$
$$=\dfrac{4}{3}*12*12*12* 3.14$$
$$=\dfrac{4}{3}*1728*3.14$$
$$=\dfrac{21703.68}{3}$$
$$=7234.56\ m^3$$
Question 5
1 / -0

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.

A
$$4$$ mm

B
$$3$$ mm

C
$$1$$ mm

D
$$8$$ mm

Solution

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 $$=2r=8\ mm$$.
Question 6
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The volume of a sphere is $$\displaystyle 300\pi { cm }^{ 3 }$$. Find its radius.

A
$$3.313$$ cm

B
$$6.313$$ cm

C
$$6.08$$ cm

D
$$4.313$$ cm

Solution

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)

$$\Rightarrow \dfrac{300*3}{4}= r^3$$
$$\Rightarrow r^3=\dfrac{900}{4}$$

$$\Rightarrow r^3=225$$
$$\Rightarrow r=\sqrt[3]{225}$$
$$\Rightarrow r=6.08\ cm$$
Question 7
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Find the volume of a sphere whose diameter is $$10$$ in.

A
$$\displaystyle 523.33\ in$$

B
$$\displaystyle 503.33{\ in }^{ 3 }$$

C
$$\displaystyle 423.33{\ in }^{ 3 }$$

D
$$\displaystyle 523.33{\ in }^{ 3 }$$

Solution

Formula:
Volume of sphere =$$\dfrac{4}{3} \pi r^3$$
$$r=radius$$
Given:
$$diameter(d)=10\ in$$
$$radius(r)=\dfrac{d}{2}=\dfrac{10}{2}=5\ in$$
$$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}*3.14*5^3$$
$$=\dfrac{4}{3}*5*5*5*3.14$$
$$=\dfrac{4}{3}*125*3.14$$
$$=\dfrac{1570}{3}$$
$$=523.33\ in^3$$
Question 8
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The volume of a sphere is $$\displaystyle 4000\pi { m }^{ 3 }$$. Find its surface area. (use $$\displaystyle \pi =\pi $$.)

A
$$\displaystyle 831.7456{ \ m }^{ 2 }$$

B
$$\displaystyle2611.68{ \ m }^{ 2 }$$

C
$$\displaystyle 631.7456{ \ m }^{ 2 }$$

D
$$\displaystyle 801.7456{\ m }^{ 2 }$$

Solution

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 $$\displaystyle =4\pi { r }^{ 2 }$$
$$\displaystyle =4\times \pi \times 14.42\times 14.42$$
$$\displaystyle =2611.68{ m }^{ 2 }$$
Question 9
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Find the volume of a hemisphere whose radius is $$7$$ cm. (use $$\displaystyle \pi =\frac { 22 }{ 7 } $$)

A
$$\displaystyle 112.66{ \ cm }^{ 3 }$$

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

C
$$\displaystyle 12.66{ \ cm }^{ 3 }$$

D
$$\displaystyle 132.66{ \ cm }^{ 3 }$$

Solution

Given, radius of hemisphere $$=7$$ cm
Volume of hemisphere $$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$$
$$\displaystyle =\frac { 2 }{ 3 } \times \frac { 22 }{ 7 } \times 7\times 7\times 7$$
$$\displaystyle =718.66{ cm }^{ 3 }$$
Question 10
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Calculate the surface area and volume of the sphere with diameter $$0.8$$ in (use $$\displaystyle \pi =3$$).

A
$$\displaystyle V=0.156{\ in }^{ 3 }$$ and $$ A=1.92{\ in }^{ 2 }$$

B
$$\displaystyle V=0.256{\ in }^{ 3 }$$ and $$ A=0.92{\ in }^{ 2 }$$

C
$$\displaystyle V=0.256{\ in }^{ 3 }$$ and $$ A=1.92{ \ in }^{ 2 }$$

D
$$\displaystyle V=0.156\ { in }^{ 3 }$$ and $$ A=2.92{\ in }^{ 2 }$$

Solution

$$\displaystyle \therefore $$ 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 $$\displaystyle =4\pi { r }^{ 2 }$$
$$\displaystyle =4\times 3\times 0.4\times .4$$
$$\displaystyle =1.92{\ in }^{ 2 }$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 39

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Surface Areas and Volumes Test - 39

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SHARING IS CARING

Question 1

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

$$56\pi \text{ cm}^3$$

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

$$46\pi {\text{ cm} }^{ 3 }$$

Solution

Question 2

$$\displaystyle 1,13,140{\ m }^{ 3 }$$

$$\displaystyle 1,13,040{\ m }^{ 3 }$$

$$\displaystyle 1,03,040{\ m }^{ 3 }$$

$$\displaystyle 2,13,040{\ m }^{ 3 }$$

Solution

Question 3

$$2$$ cm

$$5$$ cm

$$6$$ cm

$$7 $$ cm

Solution

Question 4

$$\displaystyle 7134.56{\ m }^{ 3 }$$

$$\displaystyle 7234.56{\ m }^{ 3 }$$

$$\displaystyle 7034.56{ \ m }^{ 3 }$$

$$\displaystyle 7334.56{ \ m }^{ 3 }$$

Solution

Question 5

$$4$$ mm

$$3$$ mm

$$1$$ mm

$$8$$ mm

Solution

Question 6

$$3.313$$ cm

$$6.313$$ cm

$$6.08$$ cm

$$4.313$$ cm

Solution

Question 7

$$\displaystyle 523.33\ in$$

$$\displaystyle 503.33{\ in }^{ 3 }$$

$$\displaystyle 423.33{\ in }^{ 3 }$$

$$\displaystyle 523.33{\ in }^{ 3 }$$

Solution

Question 8

$$\displaystyle 831.7456{ \ m }^{ 2 }$$

$$\displaystyle2611.68{ \ m }^{ 2 }$$

$$\displaystyle 631.7456{ \ m }^{ 2 }$$

$$\displaystyle 801.7456{\ m }^{ 2 }$$

Solution

Question 9

$$\displaystyle 112.66{ \ cm }^{ 3 }$$

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

$$\displaystyle 12.66{ \ cm }^{ 3 }$$

$$\displaystyle 132.66{ \ cm }^{ 3 }$$

Solution

Question 10

$$\displaystyle V=0.156{\ in }^{ 3 }$$ and $$ A=1.92{\ in }^{ 2 }$$

$$\displaystyle V=0.256{\ in }^{ 3 }$$ and $$ A=0.92{\ in }^{ 2 }$$

$$\displaystyle V=0.256{\ in }^{ 3 }$$ and $$ A=1.92{ \ in }^{ 2 }$$

$$\displaystyle V=0.156\ { in }^{ 3 }$$ and $$ A=2.92{\ in }^{ 2 }$$

Solution

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