Question:
A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.
Solution:
Surface area of ball
$=4 \pi r^{2}$
$=4 \pi\left(\frac{4.2}{2}\right)^{2}$
$=17.64 \pi \mathrm{cm}^{2}$
Total surface area exposed
$=\mathrm{SA}$ of ball $-200\left(\pi \mathrm{r}^{2}-\frac{4 \pi r^{2}}{2}\right)$
$=17.64 \pi-200 \pi r^{2}$
$=17.64 \pi-8 \pi$
$=80.5 \mathrm{~cm}^{2}$
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