Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5cm and height 4 cm.How many bottles are needed to empty the bowl?

Answer 1

Given :

Radius of hemispherical bowl = 9 cm

Volume of hemisphere $=$ $\frac{2}{3}$ × $\pi$×$r^3$

$=$ $\frac{2}{3}$ × $\pi$ × 9 × 9 × 9

$=$ 486$\pi$

Since height of the bottle $\left(h\right)=4$cm and Diameter of the cylindrical bottles$=3$cm

$\Rightarrow$ Radius $=1.5$cm $=\frac{3}{2}$cm

Hence ,

The volume of the cylindrical bottle $=$ $\pi$×$r^2$ × h

$=$ $\pi$ × $\frac{3}{2}$ × $\frac{3}{2}$ × 4
$=9$ $\pi$

Required number of bottles $=$ $\frac{volumeofhemisphere}{volumeofbottle}$
$=$ $\frac{486\pi }{9\pi }$
$=54$
Therefore, 54 bottles are required to fill the empty bowl.