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

Answer 1

(d) 0.36 cm³
Radius of the capsule
$=\frac{0.5}{2}\text{cm}$
= 0.25 cm

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

Then,

$$\begin{gathered} 0.25+x+0.25=2 \\ \Rightarrow 0.5+x=2 \\ \Rightarrow x=1.5 \end{gathered}$$

Hence, the capacity of the capsule$=2\times \left(\text{Volume of the hemisphere}\right)+\left(\text{Volume of the cylinder}\right)$
$=\left(2\times \frac{2}{3}\mathrm{\pi }r\right)$³+πr²h
$=\left({\displaystyle \frac{4}{3}}\times {\displaystyle \frac{22}{7}}\times {\displaystyle \frac{1}{4}}\times {\displaystyle \frac{1}{4}}\times {\displaystyle \frac{1}{4}}\right)+\left({\displaystyle \frac{22}{7}}\times {\displaystyle \frac{1}{4}}\times {\displaystyle \frac{1}{4}}\times 1.5\right)\left[\text{Since}0.25={\displaystyle \frac{1}{4}}\right]$
$=\left({\displaystyle \frac{11}{168}}+{\displaystyle \frac{33}{112}}\right)\text{cm}$³
$=\frac{121}{336}\text{cm}$³ = 0.36 cm³