**Example 1 :**

Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 g/cm^{3}. (Mass = Volume x Density)

**Solution :**

radius of spherical ball = 0.7 cm

Volume of one spherical ball = (4/3) Π r^{3}

= (4/3) (22/7) ^{ }⋅ 0.7^{ }⋅ 0.7^{ }⋅ 0.7

= 4.312/3

= 1.437

Volume of 200 steel spherical ball = 200^{ }⋅ 1.437

= 287.46 cm^{3}

1 cm³ = 7.95 g

Therefore mass of 200 spherical ball bearings

= 287.46 (7.95)

= 2285.307 gram

1000 gram = 1 kg

= 2285.307/1000

= 2.29 kg

Volume of 200 spherical balls = 2.29 kg

**Example 2 :**

The outer and inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume.

**Solution :**

From this information we have to find the volume

Outer radius (R) = 12 cm

Inner radius (r) = 10 cm

Volume of hollow sphere = (4/3) Π (R^{3}-r^{3})

= (4/3)(22/7) (12^{3}-10^{3})

= (88/21) (1728-1000)

= (88/21) (728)

= (64064/21)

= 3050.67 cm^{3}

Volume of hollow sphere is 3050.67 cm^{3}.

**Example 3 :**

The volume of a solid hemisphere is 1152 Π cu.cm. Find its curved surface area.

**Solution :**

Volume of hollow sphere = 1152 Π

(2/3) Π r^{3} = 1152 Π

r^{3} = 1152 Π (3/2Π)

r^{3 }= (576 **x** 3)/2

r^{3} = 1728

r = ∛1728

r = 12 cm

Curved surface area = 2Πr^{2}

= 2Π(12)^{2}

= 2Π(144)

= 288Π cm^{3}

Curved surface area = 288Π cm^{3}

**Example 4 :**

Find the volume of the largest right circular cone that can be cut of a cube whose edge is 14 cm.

**Solution :**

Since it is cube length of all sides will be equal that is 14 cm. Diameter and height of cone are 14 cm.

r = 14/2 ==> 7

h = 14 cm

Volume of cone = (1/3) Π r^{2} h

= (1/3) ⋅ (22/7) ^{ }⋅ 7^{2} ⋅ 14

= (1/3) ⋅ 22^{ }⋅ 49 ⋅ 2

= (49^{ }⋅ 44)/3

= 2156/3

= 718.67 cm^{3}

Volume of cone is 718.67 cm^{3}.

**Example 5 :**

The radius of a spherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

**Solution :**

Let r₁ and r₂ are the radii of two spherical balloon

r_{1} : r_{2} = 7 : 14

Volume of one spherical balloon = (4/3) Π r^{3}

(4/3) Π (7)^{3} : (4/3) Π 14^{3}

7^{3 }: 14^{3}

7 ⋅ 7 ⋅ 7 : 14 ⋅ 14 ⋅ 14

1 : 8

So, the required ratio is 1 : 8.

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