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Example – 10. The diameter of a sphere is 21 cm. Calculate its volume and surface area. (Use π = 22/7).

Solution :-  Here, r = 21/2 cm = 10.5 cm.

Volume of sphere = (4/3)πr³ = (4/3)(22/7)(10.5)³

=  4851 cm³.

Surface area of the sphere = 4πr² =(4)(22/7)(10.5)²

= 1386 cm².

Example – 11. The volume of a sphere is 38808 cm³. Find its radius and curved surface area. (Use π = 22/7).

Solution :- Volume of sphere = (4/3)πr³ = 38808
                                          r³ = (38808)(7/22)(3/4)
                                   Or, r³  = 9261
                                   Or, r   = 21 cm.
                  Surface area of the sphere = 4πr2 = (4)(22/7)(21)²
                                                                        = 5544cm².

Example – 12. Two solid spheres of same metal have weights 5920 gms and 740 gms respectively. Determine the radius of the heavier sphere if the diameter of lighter one is 5 cm.                  

Solution :-  Sphere are made of same metal. Let volume of heavier sphere be V₁ and that of lighter sphere be V₂ and their radii be r₁ and r₂ respectively.

(density × V₁)/(density × V₂) = (weight of heavy )/(weight of light)
                                                               V₁/V₂ = (5920)/(740) = 8

Or,   {(4/3)πr₁³}/{(4/3)πr₂³}= 8

Or,                         (r₁/r₂)3 = 8

Or,                      1³/(5/2)² = 8

Or,                            r₁³ = 125

Or,                            r₁ = 5

Thus radius of the lighter sphere is 5 cm.