Question

A hemispherical bowl of internal diameter $36$ cm is filled with some liquid. This liquid is to be filled into Cylinder shaped bottles each of radius $3$ cm and height $6$ cm. Find the number of bottles required to empty the bowl.

Answer 1

Radius of hemispherical bowl $=18$ cm

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

Radius of cylindrical bottle $=3$ cm

Height of cylindrical bottle $=6$ cm

Volume of cylindrical bottle = $(\pi \times 3^2\times 6)$ $c{m}^3$

Suppose $x$ bottles are required to empty the bowl.

Volume of $x$ cylindrical bottles = $(\pi \times 9\times 6\times x)$ $c{m}^3$

Volume of liquid in $x$ bottles = Volume of bowl

$\pi \times 54\times x=\frac{2\pi }{3}\times (18{)}^3$

$x=72$

Hence, $72$ bottles are required to empty the bowl.