Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

Find the volume of a hemisphere of radius $$7\;dm$$.

A
$$708.67\;dm^3$$

B
$$818.67\;dm^3$$

C
$$717.67\;dm^3$$

D
$$718.67\;dm^3$$

Solution

Volume of hemisphere $$=$$ $$\dfrac { 2 }{ 3 } \pi { r }^{ 3 }=\dfrac { 2 }{ 3 } \times \dfrac { 22 }{ 7 } \times 7\times 7\times 7$$

$$ =$$ $$718.67$$ $${ dm }^{ 3 }$$
Question 2
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Diameter of a football is $$28\;cm$$. It is made up of small hexagones each of area $$112\;cm^2$$. Find the number of small hexagones used in football.

A
$$21$$

B
$$27$$

C
$$23$$

D
$$22$$

Solution

Given, diameter of football $$=28cm$$.
Then, radius of football $$=14cm$$.
$$\therefore $$ Area of football $$=4\pi { r }^{ 2 }=4\times \dfrac { 22 }{ 7 } \times 14\times 14=2464{ cm }^{ 2 }$$.
Given, area of each hexagon $$=112{ cm }^{ 2 }$$
Number of hexagon $$=\dfrac { 2464 }{ 112 } =22$$.
Hence, option $$D$$ is correct.
Question 3
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Diameter of a sphere is $$21$$ dm. Find its surface area.

A
$$1286\;dm^2$$

B
$$1376\;dm^2$$

C
$$1386\;dm^2$$

D
$$1380\;dm^2$$

Solution

Given, diameter of a sphere, $$d=21$$ dm,
$$\therefore$$ radius of the sphere, $$r=\dfrac{d}{2}=\dfrac{21}{2}=10.5 $$ dm
Surface area of sphere $$=4 \pi r^2$$
$$=4 \pi (10.5)^2=4 \times \dfrac{22}{7} \times (10.5)^2$$
$$=1386 dm^2$$.
Therefore, option $$C$$ is correct.
Question 4
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Which one of the following statement is INCORRECT?

A
A cyclic parallelogram is a rectangle.

B
Set of points joining the middle points of all parallel chords of a circle constitute the longest chord of the circle.

C
Total surface area of a solid hemisphere is $$2\pi r^{2} .$$

D
A fair coin is tossed the chance that it shows up head is $$50\%.$$

Solution

Total surface area of a solid hemisphere is equal to the sum of curved surface area of the hemisphere and the area of the circular base.

So,
Total surface area $$=$$ $$ 2 \pi r^2 + \pi r^2$$
$$=3 \pi r^2$$
Question 5
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A hemispherical tank has inner radius of $$1.05\;m$$. Find its capacity in litres.

A
$$2425.51$$

B
$$2657.15$$

C
$$1236.5$$

D
None of these

Solution

Capacity of tank $$=$$ volume of tank
Volume of hemispherical tank $$=\dfrac { 2 }{ 3 } \pi { r }^{ 3 }$$
Given $$r=1.05\ m$$
Capacity of the tank$$=\dfrac { 2 }{ 3 } \times \dfrac { 22 }{ 7 } \times 1.05\times 1.05\times 1.05$$

$$=2.4255\ { m }^{ 3 }=2425.5\ litres$$
Question 6
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The area of the curved surface of a sphere is $$5544\;m^2$$. Find the radius of the sphere.

A
$$12$$ m

B
$$20$$ m

C
$$22$$ m

D
$$21$$ m

Solution

Given, area of curved surface of a sphere $$=5544$$ $$cm^2$$
We know, curved surface area of sphere $$=4 \pi r^2$$
$$\Rightarrow 5544=4 \times \dfrac {22}{7}\times r^2$$
$$\Rightarrow 7 \times 5544=4 \times 22\times r^2$$
$$\Rightarrow r^2=441$$
$$\Rightarrow r=21 m$$.
Therefore, option $$D$$ is correct.
Question 7
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Find the surface area of the following cubes with length of edge
$$4\;cm$$
$$3.2\;cm$$

A
$$96\;cm^2\;;\;61.44\;cm^2$$

B
$$90\;cm^2\;;\;61.44\;cm^2$$

C
$$96\;cm^2\;;\;60.44\;cm^2$$

D
$$92\;cm^2\;;\;61.44\;cm^2$$

Solution

Total surface area$$=6(4^2)=96 cm^2$$,for edge=4$$ cm^2$$
Total surface area$$=6(3.2^2)=61.44 cm^2$$, for edge=61.44 $$cm^2$$
Question 8
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The sum of the radius of the base and the height of a solid cylinder is $$37 m$$. If the total surface area of the cylinder be $$1628 sq. m$$, then its volume is:

A
$$4620m^{3}$$

B
$$4630 m^{3}$$

C
$$4520 m^{3}$$

D
$$4830 m^{3}$$

Solution

Given, $$r + h = 37 m$$
Total Surface Area of a Cylinder $$ = 2\pi r(r + h)$$
Given, $$ 2\times \cfrac {7}{22} \times r \times 37 =1628 $$
$$\Rightarrow r= \cfrac {1628 \times 7}{22 \times 37 \times 2} =7 m $$
Height (H) $$ = 37 - r = 37 -7 = 30 m $$
Volume of a Cylinder $$ = \pi { R }^{ 2 }h $$ $$ = \cfrac {22}{7} \times 7 \times 7 \times 30 = 4620 {m}^{3} $$
Question 9
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The volume of a hemispherical ball is given by the $$\displaystyle V=\frac{2}{3}\pi r^{3}$$ where $$V$$ is the volume and $$r$$ is the radius Find the diameter of he hemisphere whose volume is $$\displaystyle \frac{468512}{21}m^{3}$$

A
$$22 m$$

B
$$11 m$$

C
$$33 m$$

D
$$44 m$$

Solution

$$
V\quad =\quad \dfrac { 2 }{ 3 } \pi { r }^{ 3 }\\ \\ \dfrac { 2 }{ 3 } \pi { r }^{ 3 }\quad =\quad \dfrac { 468512 }{ 21 } \\ { r }^{ 3 }\quad =\quad \dfrac { 468512 }{ 21 } \quad \left(\dfrac { 3 }{ 2\pi } \right)\quad \\=\quad \dfrac { 468512 }{ 2\times 22 } \quad \\=10648\quad cu.m\\ r\quad =\quad \sqrt [ 3 ]{ 10648 } \quad \\=\quad 22m\\\Rightarrow Diameter\quad =\quad 44m
$$
Question 10
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Find the area covered by a road roller of width $$80\;cm$$ and diameter $$140\;cm$$ in $$40$$ revolutions.

A
$$130.8\;m^2$$

B
$$143.6\;m^2$$

C
$$141.8\;m^2$$

D
$$140.8\;m^2$$

Solution

Curved surface area of cylinder$$=2 \pi rh=2 \pi(70)(80)=35200 cm^2=3.52 m^2
$$
Area of 40 revolutions$$=3.52 \times 40=140.8 m^2$$

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Surface Areas and Volumes Test - 29

Result

Surface Areas and Volumes Test - 29

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SHARING IS CARING

Question 1

$$708.67\;dm^3$$

$$818.67\;dm^3$$

$$717.67\;dm^3$$

$$718.67\;dm^3$$

Solution

Question 2

$$21$$

$$27$$

$$23$$

$$22$$

Solution

Question 3

$$1286\;dm^2$$

$$1376\;dm^2$$

$$1386\;dm^2$$

$$1380\;dm^2$$

Solution

Question 4

A cyclic parallelogram is a rectangle.

Set of points joining the middle points of all parallel chords of a circle constitute the longest chord of the circle.

Total surface area of a solid hemisphere is $$2\pi r^{2} .$$

A fair coin is tossed the chance that it shows up head is $$50\%.$$

Solution

Question 5

$$2425.51$$

$$2657.15$$

$$1236.5$$

None of these

Solution

Question 6

$$12$$ m

$$20$$ m

$$22$$ m

$$21$$ m

Solution

Question 7

$$96\;cm^2\;;\;61.44\;cm^2$$

$$90\;cm^2\;;\;61.44\;cm^2$$

$$96\;cm^2\;;\;60.44\;cm^2$$

$$92\;cm^2\;;\;61.44\;cm^2$$

Solution

Question 8

$$4620m^{3}$$

$$4630 m^{3}$$

$$4520 m^{3}$$

$$4830 m^{3}$$

Solution

Question 9

$$22 m$$

$$11 m$$

$$33 m$$

$$44 m$$

Solution

Question 10

$$130.8\;m^2$$

$$143.6\;m^2$$

$$141.8\;m^2$$

$$140.8\;m^2$$

Solution

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