Question

There are $42$ hemispherical bowls, each of radius $3.5cm$. Find the quantity of water in litres which is just sufficient to fill these $42$ bowls. (Take $\pi =\frac{22}{7}$)

• A. $3.773$ litres
• B. $3.553$ litres
• C. $3.223$ litres
• D. $4.773$ litres

Answer 1

Answer: (A)

$3.773$ litres

Here $r=3.5cm=\frac{7}{2}cm$
Volume o fone bowl i.e., capacity of one bowl$=\frac{2}{3}$
$\pi r^3=\frac{2}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}{cm}^3=\frac{11\times 49}{6}{cm}^3$
Capacity of $42$ bowls
$=\frac{11\times 49}{6}\times 42{cm}^3=3773{cm}^3$
Thus, the required quantity of water to fill the $42$ bowl$=\frac{3773}{1000}litres=3.773litres$
Therefore, $3.773$ litres of water is just sufficient.