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 assuming that the dimples are hemispherical.

Answer 1

Diameter of golf ball$=4.1cm$

Radius of golf ball$,r=\frac{4.1}{2}=2.05cm$

Surface area of ball$=4\pi r^2=4\pi \times {\left(2.05\right)}^2=16.81\pi {cm}^2$

Radius of each dimple$=2mm=0.2cm$

Area of $150$ dimples$=150\times 2\pi r^2=150\times 2\times \pi \times {\left(0.2\right)}^2=12\pi {cm}^2$

Area of flat surface removed to make $1$ dimple$=0.04\pi {cm}^2$

$\therefore$Area of flat surface removed to make $150$ dimples$=150\times 0.04\pi$

$=6\pi {cm}^2$

TSA of golf ball exposed to surroundings$=16.81\pi +12\pi -6\pi$

$=22.81\pi =22.81\times \frac{22}{7}$

$=71.70{cm}^2$