Question

a golf ball has diameter equal to 4.1cm. its surface has 150 dimples each of radius 2mm (0.2 cm). calculate total surface area which is exposed to surroundings assuming that the dimples are hemispherical.

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