Question

A capsule of medicine is in the shape of a sphere of diameter $3.5mm$. How much medicine (in ${mm}^3$) is needed to fill this capsule?

• A. $22.458{mm}^3$
• B. $32.346{mm}^3$
• C. $23.346{mm}^3$
• D. $12.346{mm}^3$

Answer 1

Answer: (A)

The correct option is A $22.458{mm}^3$
$r=\frac{3.5}{2}mm$
Capacity of the capsule $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times \frac{3.5}{2}\times \frac{3.5}{2}\times \frac{3.5}{2}{mm}^3$
$=\frac{4}{3}\times \frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times \frac{7}{4}{mm}^3=\frac{11}{24}\times 49{mm}^3$
$=\frac{539}{24}{mm}^3=22.346{mm}^3$