Question

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the cylindrical part of the capsule is $14mm$ and the diatmeter of hemisphere is $6mm$, then find the volume of medicine capsule.

Answer 1

Given that:

Height of the cylindrical part of the capsule$=14mm$

Diameter of hemispherical part of the capsule$=6mm$

To find:

Volume of the medicine capsule$=?$

Solution:

Radius of hemispherical part of the capsule$=\frac{6}{2}mm=3mm$

Volume of the medicine capsule$=$ Volume of cylindrical part of the capsule$+$ $2\times$ Volume of hemispherical part of the capsule

$=\pi r^{2}h+2\times \frac{2}{3}\pi r^3$

$=\frac{22}{7}\times (3{)}^2\times 14m{m}^3+2\times \frac{2}{3}\times \frac{22}{7}\times (3{)}^{3}m{m}^3$ Take $(\pi =\frac{22}{7})$

$=396m{m}^3+113.144m{m}^3$

$=509.144m{m}^3$

Therefore, Volume of the medicine capsule$=509.144m{m}^3$