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 / cm3, 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 r3
V = 4 /3 x 3.14 x 4.9.x 4.9 x 4.9
V = 492 .55 cm3
Density = 7.8 g / cm3
∴ 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 mm3) is needed to fill this capsule?
Solution : Diameter = 3.5 mm
∴ radius = r = 3.5 /2 = 1.75 mm =
Volume = 4/3 π r3
⇒ V= 4/3 x 3.14 x ( 1.75)3
⇒ V = 22.44 mm3
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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 r3
∴ Volume of 27 spheres = 27 (4/3 π r3 )
Volume of new sphere = 4/3 π r’3
∴ 4/3 π r’3 = 27 (4/3 π r3)
∴ r’3 = 27 r3
∴ r’ = 3r
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4) Find the volume of a sphere whose surface area is 154 cm2.
Solution : Surface area = 154 cm2
S = 4 π r2
154 = 4 π r2
r2 = 154 / 4π
∴ r2 = 12.26
∴ r = 3.5 cm
Volume = 4/ 3 π r3
V = 4 / 3 x 3.14 x (3.5)3
∴ V = 179. 50 cm3

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

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