# 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 r3

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

From Sphere to Mensuration