Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

If the curved surface area of a solid right circular cylinder of height $$h$$ and radius $$r$$ is one-third of its total surface area, then

A
$$\displaystyle h\, =\, \frac{1}{3}\, r$$

B
$$\displaystyle h\, =\, \frac{1}{2}\, r$$

C
$$h = r$$

D
$$h = 2r$$

Solution

We know, curved surface area of a cylinder of radius "$$R$$" and height "$$h$$" $$= 2\pi Rh$$
Total surface area of a cylinder of radius "$$r$$" and height "$$h$$" $$
= 2\pi r(r + h)$$
Given, $$ 2\pi Rh = \dfrac { 1 }{ 3 } \times 2\pi r(r+h) $$
$$ \therefore h = \dfrac { 1 }{ 3 } \times (r+h) $$
$$ \therefore \dfrac { 2 }{ 3 } h = \dfrac { 1 }{ 3 } r $$
$$\therefore h =\displaystyle \dfrac { 1 }{ 2 } r$$
Question 2
1 / -0

A hemispherical bowl is made of steel, $$0.25cm$$ thick. The inner radius of the bowl is $$5cm$$. Find the outer curved surface area of the bowl.

A
$$173\ {cm}^{2}$$

B
$$133\ {cm}^{2}$$

C
$$143\ {cm}^{2}$$

D
$$273\ {cm}^{2}$$

Solution

$$r=5cm$$, thickness of steel sheet $$=0.25cm$$

$$\Rightarrow$$ $$R=5cm+0.25cm=5.25cm$$

outer curved surface area of the bowl $$=2\pi {R}^{2}$$

$$=2\times \cfrac{22}{7}\times \cfrac{525}{100}\times \cfrac {525}{100}{cm}^{2}=173.25{cm}^{2}$$
Question 3
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Find the surface area of sphere of diameter $$14$$ cm.

A
$$616{cm}^{2}$$

B
$$661\ cm^2$$

C
$$166\ cm^2$$

D
None of these

Solution

Given, diameter $$d=14$$ cm.
$$\therefore$$ radius $$ = \dfrac {d}{2} = \dfrac {14}{2} = 7 $$ cm
Surface area of a sphere of radius $$r$$ $$ = 4\pi { r }^{ 2 }$$
$$= 4 \times \dfrac {22}{7} \times 7 \times 7 $$
$$= 616 {cm}^{2} $$.
Therefore, option $$A$$ is correct.
Question 4
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Find the volume of a sphere whose radius is $$0.63m$$

A
$$1.05{m}^{3}$$

B
$$3.05{m}^{3}$$

C
$$1.15{m}^{3}$$

D
$$2.05{m}^{3}$$

Solution

$$r=0.63m$$
Volume$$=\cfrac{4}{3}\times {22}{7}\times {(0.63)}^{3}{m}^{3}$$
$$=1.047816{m}^{3}=1.05{m}^{3}$$ (approximately)
Question 5
1 / -0

Find the amount of water displaced by a solid spherical ball of diameter $$28cm$$.

A
$$11498\cfrac{2}{3}{cm}^{3}$$

B
$$11498\cfrac{2}{7}{cm}^{3}$$

C
$$11498\cfrac{1}{3}{cm}^{3}$$

D
$$11498\cfrac{2}{5}{cm}^{3}$$

Solution

Radius of the spherical ball $$ = \cfrac {28}{2} = 14 cm $$
The amount of water it displaces is equal to its volume.
Volume of a spherical ball $$ = \cfrac { 4 }{ 3 } \pi {r }^{ 3 }$$
'$$= \cfrac {4}{3} \times \cfrac {22}{7} \times 14 \times 14 \times 14$$
$$ = \cfrac { 34496 }{3} = 11498\cfrac 23 {cm}^{3} $$
Question 6
1 / -0

Find the surface area of a sphere of radius $$14$$ cm.

A
$$2464\ {cm}^{2}$$

B
$$1446\ cm^2$$

C
$$2446\ cm^2$$

D
$$2664\ cm^2$$

Solution

We know that the surface area of sphere with radius $$r$$ is $$A=4πr^{ 2 }$$.

It is given that the radius of the sphere is $$14 cm$$.

Then, $$A=4πr^{ 2 }=4\times \dfrac { 22 }{ 7 } \times (14)^{ 2 }=4\times \dfrac { 22 }{ 7 } \times 196=2464$$ $$cm^2$$.

Hence, the surface area of sphere is $$2464$$ $$cm^2$$.
Therefore, option $$A$$ is correct.
Question 7
1 / -0

Find the total surface area of a hemisphere of radius $$10$$ cm. (Use $$\pi =3.14$$)

A
$$942{cm}^{2}$$

B
$$492\ cm^2$$

C
$$249\ cm^2$$

D
$$924\ cm^2$$

Solution

Given, radius $$r=10$$ cm
Total surface area of a hemisphere of radius '$$r$$' $$ = 3\pi { r }^{ 2 } $$
Hence, total surface area of this hemisphere $$ = 3 \times 3.14 \times 10 \times 10$$
$$

= 942$$ sq.cm
Question 8
1 / -0

Find the radius of a sphere whose surface area is $$154{cm}^{2}.$$

A
$$3.5$$ cm

B
$$4.5$$ cm

C
$$4$$ cm

D
$$3$$ cm

Solution

Given, surface area of sphere $$=154 cm^2$$
Surface area of a sphere of radius '$$r$$' $$ = 4\pi { r }^{ 2 } = 154 $$
$$ \Rightarrow 4 \times \dfrac {22}{7}

\times { r }^{ 2 } = 154 {cm}^{2} $$
$$ \Rightarrow { r }^{ 2 } = \dfrac {49}{4} $$
$$\Rightarrow r = \dfrac {7}{2} = 3.5 cm$$.
Therefore, option $$A$$ is correct.
Question 9
1 / -0

It costs Rs.$$2200$$ to paint the inner curved surface of a cylindrical vessel $$10\ m$$ deep. If the cost of painting is at the rate of Rs.$$20$$ per $${m}^{2}$$.Find Inner curved surface area of the vessel.

A
$$110\ {m}^{2}$$

B
$$140\ {m}^{2}$$

C
$$210\ {m}^{2}$$

D
$$120\ {m}^{2}$$

Solution

Total cost of point$$=Rs.2200$$
cost of painting $$ 1{ m }^{ 2 }\quad is\quad Rs.20.$$
$$ \therefore$$ total area painted$$=\cfrac { 2200 }{ 20 } =110{ m }^{ 2 }$$
therefore inner curved surface area is $$ 110{ m }^{ 2 }.$$
Question 10
1 / -0

A match box measures $$4\ cm\times 2.4\ cm\times 1.5\ cm$$. What will be the volume of a packet containing $$12$$ such boxes?

A
$$172.8\ {cm}^{3}$$

B
$$120\ {cm}^{3}$$

C
$$280\ {cm}^{3}$$

D
$$360\ {cm}^{3}$$

Solution

Volume of 1 match box$$=(4\times 2.4\times 1.5){ cm }^{ 3 }\\ =14.4{ cm }^{ 3 }$$
volume of 12 such match box$$=14.4\times 12\\ =172.8{ cm }^{ 3 }$$

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Surface Areas and Volumes Test - 26

Result

Surface Areas and Volumes Test - 26

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SHARING IS CARING

Question 1

$$\displaystyle h\, =\, \frac{1}{3}\, r$$

$$\displaystyle h\, =\, \frac{1}{2}\, r$$

$$h = r$$

$$h = 2r$$

Solution

Question 2

$$173\ {cm}^{2}$$

$$133\ {cm}^{2}$$

$$143\ {cm}^{2}$$

$$273\ {cm}^{2}$$

Solution

Question 3

$$616{cm}^{2}$$

$$661\ cm^2$$

$$166\ cm^2$$

None of these

Solution

Question 4

$$1.05{m}^{3}$$

$$3.05{m}^{3}$$

$$1.15{m}^{3}$$

$$2.05{m}^{3}$$

Solution

Question 5

$$11498\cfrac{2}{3}{cm}^{3}$$

$$11498\cfrac{2}{7}{cm}^{3}$$

$$11498\cfrac{1}{3}{cm}^{3}$$

$$11498\cfrac{2}{5}{cm}^{3}$$

Solution

Question 6

$$2464\ {cm}^{2}$$

$$1446\ cm^2$$

$$2446\ cm^2$$

$$2664\ cm^2$$

Solution

Question 7

$$942{cm}^{2}$$

$$492\ cm^2$$

$$249\ cm^2$$

$$924\ cm^2$$

Solution

Question 8

$$3.5$$ cm

$$4.5$$ cm

$$4$$ cm

$$3$$ cm

Solution

Question 9

$$110\ {m}^{2}$$

$$140\ {m}^{2}$$

$$210\ {m}^{2}$$

$$120\ {m}^{2}$$

Solution

Question 10

$$172.8\ {cm}^{3}$$

$$120\ {cm}^{3}$$

$$280\ {cm}^{3}$$

$$360\ {cm}^{3}$$

Solution

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