A medicine-capsule is in the shape of a cylinder of diameter $0.5\ cm$ with two hemispheres stuck to each of its ends. The length of entire capsule is $2\ cm$. Find the capacity of the capsule.

Academic Mathematics NCERT Class 10

Given: A medicine-capsule is in the shape of a cylinder of diameter $0.5\ cm$ with two hemispheres stuck to each of its ends. The length of entire capsule is $2\ cm$.

To do: To find the capacity of the capsule.

Solution:

Capacity of the medicine $=$ Volume of both the hemispherical parts $+$ Volume of cylindrical part

Volume of a hemisphere of radius $r=\frac{2}{3}\pi r^3$

Volume of a cylindrical $=\pi r^2h$,

where $r$ is the radius of the base of the cylinder and $h$ is the height

The hemisphere and the cylinder will have the same radius $r =0.25\ cm$

Since total length of the toy is $2\ cm$, the length of the conical part

will be $2−0.25−0.25=1.5\ cm$

Hence, volume of the medicine $=2\times (\times \frac{22}{7}\times 0.25^3)+( \frac{22}{7}\times 0.25^2\times 1.5)$

$=\frac{22}{7}\times 0.25^2(2\times \frac{2}{3}\times 0.25+1.5)$

$=0.36\ cm^3$

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Updated on: 10-Oct-2022

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