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

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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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