Question

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

• A. $0.36c{m}^3$
• B. $0.40c{m}^3$
• C. $0.45c{m}^3$
• D. $0.30c{m}^3$

Answer 1

The correct option is A $0.36c{m}^3$

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 $=\pi r^{2}h$ 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 $=0.25cm$

Since total length of the toy is $2$ cm, the length of the conical part
will be $2-0.25-0.25=1.5cm$
Hence, Volume of the medicine $=2\times (\frac{2}{3}\times \frac{22}{7}\times {0.25}^3)+(\frac{22}{7}\times {0.25}^2\times 1.5)=\frac{22}{7}\times {0.25}^2(2\times \frac{2}{3}\times 0.25+1.5)=0.36{cm}^3$