A golf ball has a diameter of 4.1cm and the surface has 150 dimples of radius 2mm calculate the total surface area which is exposed to the surroundings. Assume the dimples are hemispherical

We have
Diametre of golf ball= 4.1cm
radius of each dimplets= 2mm
surface area of the ball =4πr
2
=4π×(
2
4.1

)
2
cm
2
=16.81cm
2

In case of each dimplets, surface area equal to πr
2
(r is the radius of each dimple) is removed from the surface of the ball where as the surface area of hemisphere i.e 2πr
2
is exposed to the surroundings

Total surface area exposed to the surroundings = surface area of the ball

−150πr
2
+150×2πr
2
=16.81π+150πr
2

=
⎩
⎪
⎨
⎪
⎧

16.81π+150π×(
10
2

)
2

⎭
⎪
⎬
⎪
⎫

cm
2
=22.81×
7
22

cm
2
=71.68cm
2