Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 42

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Weekly Quiz Competition

Question 1
1 / -0

The curved surface area of the cylinder is $$2\pi r h$$ where as surface area of the cylinder is

A
$$\pi r(r+h)$$

B
$$\pi rl(r+h)$$

C
$$2\pi r(r+h)$$

D
$$2\pi r^2l(r+h)$$

Solution

The curved surface area of the cylinder is $$2\pi r h$$ where as surface area of the cylinder is $$2\pi r(r+h)$$.
Surface area includes curved surface area and two circular bases of the cylinder.
Question 2
1 / -0

Find the volume of the hemisphere with radius $$6$$ cm.

A
$$352.16$$ $$cm^3$$

B
$$452.16$$ $$cm^3$$

C
$$252.16$$ $$cm^3$$

D
$$152.16$$ $$cm^3$$

Solution

Given, radius of hemisphere $$=6$$ cm
Volume of the hemisphere $$=$$ $$\dfrac{2}{3}\pi r^3$$
$$=$$ $$\dfrac{2}{3}\times 3.14 \times 6^3$$
$$= 452.16 $$ $$cm^3$$
Question 3
1 / -0

The radius of a hemisphere is $$10\ cm$$. Calculate it's volume.

A
$$3125.53$$ $$cm^3$$

B
$$2095.24$$ $$cm^3$$

C
$$3005.35$$ $$cm^3$$

D
$$2672.18$$ $$cm^3$$

Solution

Given,
radius of the hemisphere$$=10\ cm$$

Volume of hemisphere $$=\dfrac{2}{3}\pi r^3$$

$$=\dfrac{2}{3}\times\dfrac{22}{7}\times 10^3\ cm^3$$

$$=\dfrac{2}{3}\times\dfrac{22}{7}\times 1000\ cm^3$$

$$=2095.24\ cm^3$$

Hence, the volume of the hemisphere is $$2095.24\ cm^3$$ .
Question 4
1 / -0

What is the volume of the hemisphere with radius $$21$$ cm?

A
$$16404$$ $$cm^3$$

B
$$17404$$ $$cm^3$$

C
$$18404$$ $$cm^3$$

D
$$19404$$ $$cm^3$$

Solution

Given, radius of hemisphere $$=21$$ cm
Volume of the hemisphere $$=$$ $$\dfrac{2}{3}\pi r^3$$
$$=$$ $$\dfrac{2}{3}\times \dfrac{22}{7} \times 21^3$$
$$=$$ $$19404$$ $$cm^3$$
Question 5
1 / -0

Calculate the surface area of hemisphere having the radius of $$1.4$$ cm.

A
$$1.232\ cm^2$$

B
$$12.32\ cm^2$$

C
$$123.2\ cm^2$$

D
$$1232\ cm^2$$

Solution

Formula for surface area of the hemisphere with radius $$r$$ is $$S=2\pi r^2$$
Given , radius $$= 1.4$$ cm
$$S=2\times \cfrac{22}{7}\times 1.4^2$$
$$=12.32\ cm^2$$
Question 6
1 / -0

The diagram shows the cross section of six identical marbles touching each other on a horizontal surface.
If the volume of a mabrle is $$\dfrac{9 \pi}{2} cm^3$$, calculate the length of PQ, in cm.

A
9

B
27

C
18

D
22

Solution

Given: Volume of one marble $$=\dfrac{9\pi}{2}\ cm^3$$

Let the radius of each marble be $$r$$ cm.

Then volume of each marble $$= \dfrac{4}{3} \pi r^3$$

$$ \dfrac{9 \pi}{2} =\dfrac{4}{3} \pi r^3$$

$$r^3=\dfrac{9\pi}{2}\times \dfrac{3}{4}\times \dfrac{1}{\pi}$$

$$r^3=\dfrac{27}{8}$$

$$ {r = \dfrac{3}{2}}$$

Hence diameter of each marble $$=2\times \dfrac32=3\ cm$$

We know that

$$PQ = 6 \times $$ diameter of each marble

$$ = 6 \times 3 = 18\ cm$$
Question 7
1 / -0

The largest possible sphere is carved out of a wooden solid cube of side $$7$$ cm. Find the volume of the wood left. $$\left[\text{Use } \displaystyle \pi =\dfrac { 22 }{ 7 }\right]$$

A
$$163.3\ cm^3$$

B
$$164\ cm^3$$

C
$$165\ cm^3$$

D
$$170\ cm^3$$

Solution

For such sphere its diameter should be equal to the side of sphere.
Diameter of sphere $$= 7$$ cm

So, radius $$= 3.5 $$ cm

Volume of the sphere carved out $$= \dfrac{4}{3}\pi r^3$$

$$=\displaystyle \frac{4}{3}\times \frac{22}{7}\times 3.5^{3}$$

$$= 179.7 cm^3$$

$$\text{Volume of the cube of edge} 'a' \text{units} =a^3 \\= 7^3\\=343$$

$$\text{Volume of the wooden left} = 343 – 179.7 \\= 163.3\ cm^3$$
Question 8
1 / -0

Calculate the total surface area of the right circular cylinder shown in the above figure (in square units).

A
$$\displaystyle 300\pi $$

B
$$\displaystyle 400\pi $$

C
$$\displaystyle 500\pi $$

D
$$\displaystyle 600\pi $$

Solution

From the given figure, we can see that:
The diameter of the cylinder $$(d)=20$$ and
The height of the cylinder $$(h)=20$$
Hence, the radius of the cylinder will be $$r=\dfrac{20}{2}=10$$

We know that, the total surface area of a cylinder is $$2\pi r^2+2\pi r h$$
Here, $$r=10,\ h=20$$
$$\therefore \ $$ The total surface area $$=2\pi (10)^{2}+2\pi(10\times20)$$
$$=2\pi(100+200)$$
$$=\pi(2\times 300)$$
$$=600\pi\ square\ units$$

Hence, the total surface area of the given cylinder is $$600\pi \ square\ units$$.
Question 9
1 / -0

A hemispherical container with radius 6 cm contains 325 m$$l$$ of milk. Calculate the volume of milk that is needed to fill the container completely. $$(\pi = 3.142)$$

A
$$147.45\ ml$$

B
$$127.45\ ml$$

C
$$137.45\ ml$$

D
None

Solution

Formula for volume of Hemisphere $$V = \dfrac{2}{3}\pi r^{3} $$

$$ V = \dfrac{2}{3}\times \pi \times 6^{3} $$

$$ V = \dfrac{2}{3}\times \dfrac{22}{7} \times 216$$

$$ \Rightarrow V = 452.57\,cm^{3} $$

We know that $$1 \ ml = 1 \ cc$$

Volume $$V$$ in $$ml \ { = 452.57\,ml} $$

Given volume of milk $$=325 \ ml$$

$$ \therefore $$ Volume that should be added $$ = 452.57-325\ ml $$
$$ = {127.57\,ml} $$
Question 10
1 / -0

If the total surface area of a solid hemisphere is $$462$$ $$\displaystyle { cm }^{ 2 }$$, find its volume.
Note: Take $$\displaystyle \pi =\frac { 22 }{ 7 } $$

A
$$716$$

B
$$718.67$$

C
$$720.87$$

D
$$840$$

Solution

Total surface area of the hemisphere $$= 462 {cm}^2$$

Total surface area of the hemisphere $$= 2\pi r^2$$

$$\Rightarrow 462 = 3\pi r^2$$

$$\Rightarrow r = 7$$ cm

Volume of hemisphere $$= \dfrac{2}{3}\pi r^3$$

$$V = \dfrac{2}{3}\times \dfrac{22}{7} \times 7^3$$

$$V = 718.67 {cm}^3$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 42

Result

Surface Areas and Volumes Test - 42

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SHARING IS CARING

Question 1

$$\pi r(r+h)$$

$$\pi rl(r+h)$$

$$2\pi r(r+h)$$

$$2\pi r^2l(r+h)$$

Solution

Question 2

$$352.16$$ $$cm^3$$

$$452.16$$ $$cm^3$$

$$252.16$$ $$cm^3$$

$$152.16$$ $$cm^3$$

Solution

Question 3

$$3125.53$$ $$cm^3$$

$$2095.24$$ $$cm^3$$

$$3005.35$$ $$cm^3$$

$$2672.18$$ $$cm^3$$

Solution

Question 4

$$16404$$ $$cm^3$$

$$17404$$ $$cm^3$$

$$18404$$ $$cm^3$$

$$19404$$ $$cm^3$$

Solution

Question 5

$$1.232\ cm^2$$

$$12.32\ cm^2$$

$$123.2\ cm^2$$

$$1232\ cm^2$$

Solution

Question 6

9

27

18

22

Solution

Question 7

$$163.3\ cm^3$$

$$164\ cm^3$$

$$165\ cm^3$$

$$170\ cm^3$$

Solution

Question 8

$$\displaystyle 300\pi $$

$$\displaystyle 400\pi $$

$$\displaystyle 500\pi $$

$$\displaystyle 600\pi $$

Solution

Question 9

$$147.45\ ml$$

$$127.45\ ml$$

$$137.45\ ml$$

None

Solution

Question 10

$$716$$

$$718.67$$

$$720.87$$

$$840$$

Solution

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