Question

A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. The length of the entire capsule is $14mm$ and the diameter of the capsule is $5mm$. Find its surface area.

Answer 1

Given diameter = $5mm$

hence radius $=\frac{5}{2}=2.5mm$

Length of capsule = cylinder + 2 hemisphere = length of cylinder + 2 times the radius of hemisphere

$14mm=$ length of cylinder $+2\times 2.5$

length of cylinder $=9mm$

The total surface area of the capsule $\Rightarrow$ curved surface area of cylinder $+2\times$ curved surface area of hemisphere

Curved surface area of cylinder $=2\pi rh$

$=2\times \frac{22}{7}\times 2.5\times 9$

$\to 141.42m{m}^2$

Curved surface are of hemisphere

$=2\pi r^2=39.28m{m}^2$

$\therefore$ Total surface area of capsule

$=141.42+2\times 39.28$

$\Rightarrow 219.93\approx 220m{m}^2$