Question

A golf ball has diameter equal to 4.1 cm. Its surface has 150 dimples each of radius 2 mm. Calculate total surface area which is exposed to the surroundings. (Assume that the dimples are all hemispherical) [π = 22/7]

Answer 1

Diameter of golf ball = 4.1 cm

Radius of golf ball 

Now, surface area of golf ball without dimples 

It is given that the shape of dimples is hemispherical and radius of each dimple = 2 mm = 0.2 cm

∴ area of each dimple = 

So, area of 150 dimples = 150 × area of each dimple = 150 × 0.08π = 12π cm2

Area of flat surface removed to make 1 dimple 

∴ area of flat surface removed to make 150 dimples 

Now, total surface area of golf ball exposed to surroundings = surface area of golf ball without dimples + area of 150 dimples - area of flat surface removed to make 150 dimples

= 16.81π + 12π - 6π = 22.81π cm2