Question

A hemispherical bowl has diameter 9 cm. The liquid is poured into cylindrical bottles of diameter 3 cm and height 3 cm. If a full bowl of liquid is filled in the bottles, find how many bottles are required.

Answer 1

Given: Diameter $=9$cm , hence radius $\left(r\right)$$=$ $\frac{9}{2}$ cm

Volume of of a hemispherical bowl $=\frac{1}{2}[\frac{4}{3}\pi$$r^3]$

Here $r=$ $\frac{9}{2}$

$\Rightarrow$ Volume of hemispherical bowl $=\frac{1}{2}[\frac{4}{3}\pi$ $\left(\frac{9}{2}{)}^3\right]$

$\Rightarrow$Volume of the bowl $=\frac{243}{4}\pi$ $c{m}^3$

Now to calculate volume of each cylindrical bottle we are given:

Diameter : $3cm$ , hence $r$ $=\frac{3}{2}$ and height $\left(h\right)$ $=3$ cm

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

$\Rightarrow$volume of cylinder $=\pi$ $(\frac{3}{2}{)}^2\times 3$

$\Rightarrow$Volume of cylinder $=\frac{27}{4}\pi$ $c{m}^3$

Now a number of bottles $=$ Volume of hemispherical bowl $÷$ volume of the cylinder

$\Rightarrow$Number of bottles $=\frac{243}{4}\pi ÷\frac{27}{4}\pi$

$\Rightarrow$ Number of bottles $=9$

Hence 9 bottles are required.