Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

The diagram shows the net of a right cylinder. Find the volume of the cylinder, in cm$$^3$$

A
$$\dfrac{20}{\pi}$$

B
$$\dfrac{50}{\pi}$$

C
$$\dfrac{25}{\pi}$$

D
$$40 \pi$$
Question 2
1 / -0

A spherical iron ball of volume $$720 \:cm^3$$ is immersed in a half-filled tank as shown in the figure.
Find the rise in the water level.

A
3 cm

B
$$3\frac{1}{2}\:cm$$

C
$$4\frac{3}{4}\:cm$$

D
6

cm
Question 3
1 / -0

Sixteen cylindrical cans, each with a radius of 1 unit, are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box is square units?

A
16

B
32

C
64

D
128

Solution
Question 4
1 / -0

Find the diameter of a sphere whose volume is $$113\cfrac{1}{7}$$ cubic metres.

A
$$3m$$

B
$$5m$$

C
$$6m$$

D
$$8m$$

E
$$4m$$

Solution
Question 5
1 / -0

The weight of a sphere of iron of radius $$8cm$$ is $$1.2kg$$. What is the weight of a similar sphere whose radius is $$4cm$$?

A
$$600$$ grams

B
$$400$$ grams

C
$$150$$ grams

D
$$250$$ grams

Solution
Question 6
1 / -0

When the radius of a sphere decreases from $$3\ cm$$ to $$2.98\ cm$$ then the approximately decrease in volume of sphere is

A
$$0.002\pi \ \text{cm}^{3}$$

B
$$0.072\pi \ \text{cm}^{3}$$

C
$$0.72\pi \ \text{cm}^{3}$$

D
$$0.008\pi \ \text{cm}^{3}$$

Solution

Given radius of sphere decreases from 3 cm to 2.98 cm
volume of sphere $$ = \frac{4}{3}\pi r^{3}$$
$$ \triangle r = r_{2}-r_{1}$$
$$ = 2.98-3$$
$$ \triangle r = -0.02$$
$$ dr = -0.02 $$
consider $$ y = \frac{4}{3}\pi r^{3}$$
$$ \frac{dy}{dr} = \frac{4}{3}\pi 3r^{2}$$
$$ \frac{dy}{dr} = 4\pi r^{2}$$
$$ dy = 4\pi r^{2}.dr$$
$$ dy = 4\pi 3^{2}.(-0.02)$$
$$ dy = 4(3.14) 9(-0.02)$$
$$ dy = 36\pi (-0.02)$$
$$ dy = -0.72\pi \,cm^{3}$$
$$ \therefore $$ The volume of sphere
decrease by $$ -0.72 \pi \,cm^{3}$$
Question 7
1 / -0

Three solid metallic spheres of radii $$6$$, $$8$$ and $$10$$ centimetres are melted to form a single solid sphere. The radius of the sphere so formed is __________.

A
$$24$$cm

B
$$16$$cm

C
$$18$$cm

D
$$12$$cm

Solution

Given are three metallic spheres of radius $$6,8,10$$ cm.
They are melted to form a single solid sphere.
Now,
Volume of the single solid sphere=Volume of the three spheres
Say the radius of the resulting sphere is $$r$$ cm.
$$\therefore \cfrac { 4 }{ 3 } \pi { r }^{ 3 }=\cfrac { 4 }{ 3 } \pi { (6) }^{ 3 }+\cfrac { 4 }{ 3 } \pi { (8) }^{ 3 }+\cfrac { 4 }{ 3 } \pi { (10) }^{ 3 }\\ =>{ r }^{ 3 }={ 6 }^{ 3 }+{ 8 }^{ 3 }+{ 10 }^{ 3 }$$
$$=>r={ \left( 1728 \right) }^{ \cfrac { 1 }{ 3 } }=12$$cm
Question 8
1 / -0

The largest sphere is cut off from a cube of side 5cm. The volume of the sphere will be_

A
$$

27 \pi \mathrm{cm}^{3}

$$

B
$$

30 \pi \mathrm{cm}^{3}

$$

C
$$

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

$$

D
$$

\frac{125}{6} \pi \mathrm{cm}^{3}

$$

Solution
Question 9
1 / -0

If the surface area of a sphere is $$144\pi\ m^2$$, then its volume is

A
$$288 \pi\ m^3$$

B
$$316 \pi\ m^3$$

C
$$300 \pi\ m^3$$

D
$$188 \pi\ m^3$$

Solution

Let the radius of the sphere be $$r.$$

Surface area of a sphere $$ = 144\pi$$
$$4\pi r^2=144\pi$$
$$r^2=36$$
$$r = 6\ m$$

Now,
Volume of a sphere $$=\dfrac43 \pi r^3$$
$$=\dfrac43\pi \times 6^3$$
$$=288\pi\ m^3$$

Hence, option $$A$$ is correct.
Question 10
1 / -0

A water tank has a capacity of $$10,000$$ litre. Its value in $$m ^ { 3 }$$ is

A
10$$\mathrm { m } ^ { 3 }$$

B
1000$$\mathrm { m } ^ { 3 }$$

C
1$$\mathrm { m } ^ { 3 }$$

D
none

Solution