Question

A hemispherical bowl of internal diameter $36cm$ contains liquid. This liquid is filled into $72$ cylindrical bottles of diameter $6cm$. Find the height of each bottle, if $10\%$ liquid is wasted in this transfer.

• A. $50$ cm
• B. $5.2$ cm
• C. $5.4$ cm
• D. $6.0$ cm

Answer 1

The correct option is C $5.4$ cm

Diameter $=36$ cm, then radius $=18$ cm

Volume of hemispherical bowl $=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times (18{)}^3=12219.43c{m}^3$

Given radius of cylinder $=3$ cm

Volume of cylinder $=\pi r^{2}h$

Volume of $72$ bottles $=\frac{22}{7}\times (3{)}^2\times h\times 72$

$10\%$ of $12219.943=1221.943$ is wasted

Remaining volume of liquid $=12219.943-1221.943=10997.487{cm}^3$

$\therefore 72\times \frac{22}{7}\times 3\times 3\times h=10997.487$

$\Rightarrow h=\frac{10997.487\times 7}{72\times 22\times 9}=5.4$ cm