Question

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 $14mm$ and the diameter of the capsule is $5mm$. Find its surface area.

Answer 1

From the figure, it can be seen that, the capsule is a combination of cylinder and two hemispheres.

Total surface area of capsule will be sum of surface area of cylinders and twice the surface area of hemisphere.

From the figure, length of cylinder $=9cm$

radius of cylinder $=$ radius of hemisphere $=\frac{5}{2}$

Surface area of cylinder :

$=2\pi r\ell$

$=2\pi \left(\frac{5}{2}\right)\left(9\right)$

$=45\pi$

Surface area of two hemispheres :

$=2\times 2\pi r^2$

$=2\left(2\pi \right(\frac{5}{2}{)}^2)$

$=4\pi \frac{25}{4}$

$=25\pi$

Total surface area :

$=25\pi +45\pi$

$=70\pi c{m}^2$

$=\frac{22}{7}\times 70$

$=220c{m}^2$