Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 44

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Question 1
1 / -0

The diameter of a sphere is decreased by $$25$$%. By what percent does its curved surface area decrease?

A
$$53.85 \%$$

B
$$34.85 \%$$

C
$$45.65 \%$$

D
$$43.75 \%$$

Solution

$$\textbf{Step 1: Calculating}$$
$$\text{Let the diameter of the sphere be } r$$
$$\implies \text{Surface area}_1=\pi d^2$$
$$\textbf{Step 2: Calculating}$$
$$\text{The diameter of the sphere changes to }r'$$
$$\implies d'=d-0.25d=0.75d$$
$$\implies \text{Surface area}=\pi d'^2$$
$$\implies \text{Surface area}_2=\pi (0.75d)^2=0.5625\pi d^2$$
$$\implies \text{% Change in surface area}=\dfrac{S.A_2-S.A_1}{S.S_1}\times 100=\dfrac{(0.5625-1)\pi d^2}{(1)\pi d^2}=-43.75$$
$$\textbf{Hence, The surface area decreases by 43.75%}$$
Question 2
1 / -0

Curved surface area of solid sphere is $$24{ cm }^{ 2 }$$. If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is :

A
$$12{ cm }^{ 2 }$$

B
$$8{ cm }^{ 2 }$$

C
$$16{ cm }^{ 2 }$$

D
$$18{ cm }^{ 2 }$$

Solution

$$\text{Curved surface area of solid sphere}=4\pi r^2$$
$$\Rightarrow 4\pi r^2=24$$
$$\Rightarrow \pi r^2=6$$ ...(i)
Now, total surface area of hemisphere$$=3\pi r^2$$
$$\therefore \text{Total surface area of hemisphere}=3(6)=18cm^2$$ (from (i))
Option D is correct.
Question 3
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The total surface area of a solid hemisphere of diameter $$2$$ cm is equal to

A
$$12{cm}^{2}$$

B
$$12\pi {cm}^{2}$$

C
$$4\pi {cm}^{2}$$

D
$$3\pi {cm}^{2}$$

Solution

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

Given, diameter $$=2$$ cm
Therefore, radius $$=1$$ cm.

Therefore, total surface area is $$3\pi r^2$$
$$=3\times \pi\times (1)^2$$
$$=3\pi$$ sq.cm.
Question 4
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If the radius of a sphere is $$2\ cm$$, then the curved surface area of the sphere is equal to:

A
$$8\pi \ cm^{2}$$

B
$$16 \ cm^{2}$$

C
$$12\pi \ cm^{2}$$

D
$$16\pi \ cm^{2}$$

Solution

Curved surface area of sphere $$=4\pi r^2$$.
Here, $$r=2 cm$$.
$$\therefore$$ Curved surface area of sphere $$=4\pi (2)^2=16\pi cm^2$$.
Therefore, option $$D$$ is correct.
Question 5
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A solid right circular cylinder has a radius of $$8\ cm$$ and a height of $$14 \ cm$$. Find its curved surface area.

A
$$704 \ {cm}^{2}$$

B
$$735 \ {cm}^{2}$$

C
$$74 \ {cm}^{2}$$

D
None of these

Solution

We have,
$$h=14\ cm, r=8\ cm$$

We know that the curved surface area of the cylinder is
$$=2\pi r h$$

Let $$S$$ be the required curved surface area
$$S=2\times \dfrac{22}{7}\times 14\times 8$$

$$=704\ cm^2$$

Hence, (A) is the correct option
Question 6
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If the surface area of a sphere is $$36\pi {cm}^{2}$$, then the volume of the sphere is equal to

A
$$12\pi {cm}^{3}$$

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

C
$$72\pi {cm}^{3}$$

D
$$108\pi {cm}^{3}$$

Solution

We have,
$$surface\ area=36\pi\ cm^2$$

We know that the surface area of the sphere
$$=4\pi r^2$$

So,
$$4\pi r^2=36\pi$$

$$r^2=9$$

$$r=3\ cm$$

We know that the volume of the sphere
$$=\dfrac{4}{3}\pi r^3$$

Therefore,
$$=\dfrac{4}{3}\pi\times 3^3$$

$$=4\times \pi \times 9$$

$$=36\pi\ cm^3$$

Hence, this is the answer.
Question 7
1 / -0

The surface area of two spheres are in the ratio of $$9:25$$. Then their volumes are in the ratio

A
$$81:625$$

B
$$729:15625$$

C
$$27:75$$

D
$$27:125$$

Solution

Given,
The ratio of surface area of two sphere
$$=\dfrac{9}{25}$$

We know that the surface area of the sphere
$$=4\pi r^2$$

So,
$$\dfrac{4\pi r_1^2}{4\pi r_2^2}=\dfrac{9}{25}$$

$$\dfrac{r_1^2}{r_2^2}=\dfrac{9}{25}$$

$$\dfrac{r_1}{r_2}=\dfrac{3}{5}$$

We know that the volume of the sphere
$$=\dfrac{4}{3}\pi r^3$$

Therefore,
$$=\dfrac{\dfrac{4}{3}\pi r_1^3}{\dfrac{4}{3}\pi r_2^3}$$

$$=\dfrac{3^3}{5^3}$$

$$=\dfrac{27}{125}$$

Hence, this is the answer.
Question 8
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If the volume of a sphere is $$\cfrac{9}{16}\pi$$ $$cu.cm$$, then its radius is

A
$$\cfrac{4}{3}cm$$

B
$$\cfrac{3}{4}cm$$

C
$$\cfrac{3}{2}cm$$

D
$$\cfrac{2}{3}cm$$

Solution

We have,
$$V=\dfrac{9\pi}{16}\ cm^3$$

We know that the volume of the sphere
$$=\dfrac{4}{3}\pi r^3$$

So,
$$\dfrac{4}{3}\pi\times r^3=\dfrac{9\pi}{16}$$

$$\dfrac{4}{3} r^3=\dfrac{9}{16}$$

$$r^3=\dfrac{27}{64}$$

$$r=\dfrac{3}{4}\ cm$$

Hence, this is the answer.
Question 9
1 / -0

The inner curved surface area of a hemispherical dome of a building needs to be painted. If the circumference of the base is $$17.6\ m$$, find the cost of painting it at the rate of Rs.$$5$$ per sq.m

A
Rs.$$246.40$$

B
Rs.$$24.40$$

C
Rs.$$26.40$$

D
None of these

Solution

We have,
Circumference $$=17.6\ m$$

Circumference of circle $$= 2\pi r$$

$$17.6 = 2\times \dfrac{22}{7}\times r$$

$$44r = 17.6\times 7$$

$$r = \dfrac{123.2}{44}=2.8\ m$$

Now, Curved surface area of the hemisphere $$= 2\pi r^2$$

$$=2\times \dfrac{22}{7}\times 2.8\times 2.8$$

$$49.28\ m^2$$

Cost of painting $$= Rs.\ 5\ per\ m^2$$

Total cost of painting $$= 49.28\times 5$$

$$= Rs.\ 246.4$$

Hence, the cost of painting is $$= Rs.\ 246.4$$
Question 10
1 / -0

How many litres of water does this fish tank will hold ?

A
$$2.4$$ L

B
$$24$$ L

C
$$4.8$$ L

D
$$100$$ L

Solution

Volume$$=l \times b \times h=24 \times 20 \times 50=24000 \ \text{cm}^3$$
$$1L = 1000 \ \text{cm}^3$$
So, $$24$$ L $$=24000 \ \text{cm}^3$$
Thus $$24$$ litres of water the fish tank will hold.

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 44

Result

Surface Areas and Volumes Test - 44

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SHARING IS CARING

Question 1

$$53.85 \%$$

$$34.85 \%$$

$$45.65 \%$$

$$43.75 \%$$

Solution

Question 2

$$12{ cm }^{ 2 }$$

$$8{ cm }^{ 2 }$$

$$16{ cm }^{ 2 }$$

$$18{ cm }^{ 2 }$$

Solution

Question 3

$$12{cm}^{2}$$

$$12\pi {cm}^{2}$$

$$4\pi {cm}^{2}$$

$$3\pi {cm}^{2}$$

Solution

Question 4

$$8\pi \ cm^{2}$$

$$16 \ cm^{2}$$

$$12\pi \ cm^{2}$$

$$16\pi \ cm^{2}$$

Solution

Question 5

$$704 \ {cm}^{2}$$

$$735 \ {cm}^{2}$$

$$74 \ {cm}^{2}$$

None of these

Solution

Question 6

$$12\pi {cm}^{3}$$

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

$$72\pi {cm}^{3}$$

$$108\pi {cm}^{3}$$

Solution

Question 7

$$81:625$$

$$729:15625$$

$$27:75$$

$$27:125$$

Solution

Question 8

$$\cfrac{4}{3}cm$$

$$\cfrac{3}{4}cm$$

$$\cfrac{3}{2}cm$$

$$\cfrac{2}{3}cm$$

Solution

Question 9

Rs.$$246.40$$

Rs.$$24.40$$

Rs.$$26.40$$

None of these

Solution

Question 10

$$2.4$$ L

$$24$$ L

$$4.8$$ L

$$100$$ L

Solution

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