 # A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with a hemisphere tucked at each end.

Question:

A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with a hemisphere tucked at each end. The length of the entire capsule is 2 cm. The capacity of the capsule is
(a) 0.33 cm2
(b) 0.34 cm2
(c) 0.35 cm2
(d) 0.36 cm2

Solution:

(d) 0.36 cm3

$=\frac{0.5}{2} \mathrm{~cm}$

= 0.25 cm

Let the length of the cylindrical part of the capsule be cm.

Then,

$0.25+x+0.25=2$

$\Rightarrow 0.5+x=2$

$\Rightarrow x=1.5$

Hence, the capacity of the capsule $=2 \times$ (Volume of the hemisphere) $+$ (Volume of the cylinder)

$=\left(2 \times \frac{2}{3} \pi r\right)^{3}+\pi r^{2} h$

$=\left(\frac{4}{3} \times \frac{22}{7} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}\right)+\left(\frac{22}{7} \times \frac{1}{4} \times \frac{1}{4} \times 1.5\right) \quad\left[\right.$ Since $\left.0.25=\frac{1}{4}\right]$

$=\left(\frac{11}{168}+\frac{33}{112}\right) \mathrm{cm}^{3}$

$=\frac{121}{336} \mathrm{~cm}^{3}=0.36 \mathrm{~cm}^{3}$