Question

Question 14
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. the capacity of the capsule is
(A) $0.36c{m}^3$
(B) $0.35c{m}^3$
(C) $0.34c{m}^3$
(D) $0.33c{m}^3$

Answer 1

Given, diameter of cylinder = diameter of hemisphere = 0.5 cm
[since , both hemispheres are attach with cylinder]
$\therefore$ Radius of cylinder (r) = radius of hemisphere $\left(r\right)=\frac{0.5}{2}=0.25cm[\because diameter=2\times radius]$

And total length of capsule = 2 cm.
$\therefore$ Length of cylindrical part of capsule.
h = Length of capsule – Radius of both hemispheres

Now, capacity of capsule
= Volume of cylindrical part $+2\times$ Volume of hemisphere
$=\pi r^{2}h+2\times \frac{2}{3}\pi r^3$
$[\because Volumeofcylinder=\pi \times (radius)2\times heightandvolumeofhemisphere=\frac{2}{3}\pi (radius{)}^3=\frac{22}{7}\left[\right(0.25{)}^2\times 1.5+\frac{4}{3}\times \left(0.25{)}^3\right]=\frac{22}{7}[0.09375+0.0208]=\frac{22}{7}\times 0.11455=0.36c{m}^3\left(approx\right)$

Hence, the capacity of capsule is $0.36c{m}^3$