Question

A golf ball has diameter equal to $4.1cm$. Its surface has $150$ dimplets each of radius $2mm$. Calculate total surface area which is exposed to the surroundings assuming that the dimples are hemispherical

Answer 1

We have

Diametre of golf ball= 4.1cm

radius of each dimplets= 2mm
surface area of the ball $=4\pi r^2=4\pi \times {\left(\frac{4.1}{2}\right)}^2{cm}^2=16.81{cm}^2$

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

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

$-150\pi r^2+150\times 2\pi r^2=16.81\pi +150\pi r^2$

$=\{16.81\pi +150\pi \times {\left(\frac{2}{10}\right)}^2\}{cm}^2=22.81\times \frac{22}{7}{cm}^2=71.68{cm}^2$