# Volume of Sphere

Volume of Sphere (Sphere) can be measured using measuring jar filled with water. But the level of water in the jar does not form a straight line so the volume is not that accurate. So we will use a formula to find the Volume of Sphere. Volume - Sphere = 4/3 π r
^{3} |

**Some solved examples :**

1) A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g / cm

^{3}, find the mass of the shot-putt.

**Solution :**Since the shot-putt is a solid sphere made of metal .

Mass = Volume x density

Volume = 4/ 3 π r

^{3}

V = 4 /3 x 3.14 x 4.9.x 4.9 x 4.9

V = 492 .55 cm

^{3}

Density = 7.8 g / cm

^{3}

∴ Mass = V x D

⇒ Mass = 492.55 x 7.8 = 3841.89 g

∴ Mass = 3.84 kg

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2) A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine ( in mm

^{3}) is needed to fill this capsule?

**Solution :**Diameter = 3.5 mm

∴ radius = r = 3.5 /2 = 1.75 mm =

Volume = 4/3 π r

^{3}

⇒ V= 4/3 x 3.14 x ( 1.75)

^{3}

⇒ V = 22.44 mm

^{3}

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3) Twenty seven solid iron sphere , each of radius r and surface area S are melted to form sphere with surface area S’. Find the radius r’ of the new sphere.

**Solution :**Volume of old sphere = 4/3 π r

^{3}

∴ Volume of 27 spheres = 27 (4/3 π r

^{3})

Volume of new sphere = 4/3 π r’

^{3}

∴ 4/3 π r’

^{3}= 27 (4/3 π r

^{3})

∴ r’

^{3}= 27 r

^{3}

∴ r’ = 3r

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4) Find the volume of a sphere whose surface area is 154 cm

^{2}.

**Solution :**Surface area = 154 cm

^{2}

S = 4 π r

^{2}

154 = 4 π r

^{2}

r

^{2}= 154 / 4π

∴ r

^{2}= 12.26

∴ r = 3.5 cm

Volume = 4/ 3 π r

^{3}

V = 4 / 3 x 3.14 x (3.5)

^{3}

∴ V = 179. 50 cm

^{3}

**Volume :**

• Volume Formulas

• Volume of Irregular Shape

• Volume of Cube

• Volume of Rectangular Prism(Cuboid)

• Volume of Cylinder

• Volume of Cone

• Volume of Sphere

• Volume Hemisphere

• Volume of Prism

• Volume of Pyramid

• Volume Formulas

• Volume of Irregular Shape

• Volume of Cube

• Volume of Rectangular Prism(Cuboid)

• Volume of Cylinder

• Volume of Cone

• Volume of Sphere

• Volume Hemisphere

• Volume of Prism

• Volume of Pyramid

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