Question

A golf ball has diameter is equal to 14 centimetre. Its surface have 120 dimples each of radius 2.8 millimetre.Calculate the total surface area which is exposed to the surrounding assuming that the dimples are hemispherical.

Answer 1

Radius of the sphere = R = 14/2 = 7cm = 70 mm
Radius of the small hemisphere = r = 2.8 mm
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Area exposed to the surrounding
= Total surface are of sphere - area of 120 circles + Curved surface area of 120 hemisphere
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= 4πR^2 - 120×(πr^2) + 120×(2πr^2)
= 4πR^2 - 120πr^2 + 240πr^2
= 4πR^2 - 120πr^2
= 4π × (R^2 - 30r^2)

= 4×(22/7) × [(70×70)-(30×2.8×2.8)]
= (88/7) × (4900-235.2)
= (88/7)×4664.8
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= 58.643.2 mm sq.