Question

A medicine capsule is in the shape of a cylinder with two hemispheres 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. (Use $\pi =\frac{22}{7}$).

Answer 1

Given:
Length of Capsule (l) = $14$ mm

Diameter of Capsule = Diameter of Cylinder $=5$ mm

Radius = $\frac{Diameter}{2}$

Therefore, Radius of each Hemisphere = Radius of Cylinder = r = $\frac{5}{2}$ = 2.5 mm

Length of Cylinder = AB = Total length of Capsule - Radius of left Hemisphere - Radius of Right Hemisphere

$=14-2.5-2.5=9$ mm

Surface Area of Capsule = Curved Surface Area of Cylinder + Surface Area of Left Hemisphere + Surface Area of Right Hemisphere

$=2\pi rl+2\pi r^2+2\pi r^2$

$=2\pi rl+4\pi r^2$

$=2\times \frac{22}{7}\times 2.5\times 9+4\times \frac{22}{7}\times {2.5}^2$

$=\frac{22}{7}[45+25]=\frac{22}{7}\times 70=220$ mm${}^2$