# A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. "

Given:

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.

To do:

We have to find its surface area.

Solution:

Diameter of each hemispherical end $=5 \mathrm{~mm}$

This implies,

Radius of each hemispherical end $=\frac{5}{2} \mathrm{~mm}$

Therefore,

Surface area of each hemispherical end $=2 \pi^{2}$

$=2 \times \frac{22}{7} \times \frac{5}{2} \times \frac{5}{2}$

$=\frac{275}{7} \mathrm{~mm}^{2}$

Surface area of both hemispherical ends $=\frac{2 \times 275}{7} \mathrm{~mm}^{2}$

$=\frac{550}{7} \mathrm{~mm}^{2}$

Total length of the capsule  $=14 \mathrm{~mm}$

Length of the cylindrical surface $=$ Total length $-$ Radii of both hemispherical ends

$=14-2(\frac{5}{2})$

$=14-5$

$=9 \mathrm{~mm}$

Curved surface area of the cylindrical portion $=2 \pi r h$

$=2 \times \frac{22}{7} \times \frac{5}{2} \times 9$

$=\frac{990}{7} \mathrm{~mm}^{2}$

Total surface area of the capsule $=$ Area of both hemispherical ends $+$ Area of the cylindrical portion

$=\frac{550}{7}+\frac{990}{7}$

$=\frac{1540}{7} \mathrm{~mm}^{2}$

$=220 \mathrm{~mm}^{2}$.