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)

Answer 1

Solution:-

Diameter of the ball = 4.1 cm 
Then, radius = 4.1/2 = 2.05 cm
Now, surface area of the ball without dimples = 4πr²
= 4*π*2.05*2.05
= 16.81 sq cm
It is given that the shape of dimples is hemispherical and radius of each dimple = 2 mm or 0.2 cm
Area of each dimple = 2πr²
2*π*0.2*0.2
= 0.08π sq cm
Area of 150 dimples = 150*0.08π
= 12π sq cm
Area of flat surface to removed to make one dimple = πr²
= π*0.2*0.2
= 0.04π sq cm
∴ Area of flat surface removed to make 150 dimples = 0.04π*150
= 6π sq cm
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
= 28.81π - 6π
= 22.81π
= 22.81*3.14
= 71.62 sq cm
Answer.