Question

The innder diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

Answer 1

Volume that can hold = volume of cylinder vessel - volume of hemisphere

radius of the cylinder = radius of hemisphere = 7 cm

$\therefore Volumethatcanhold=volumeofcylindervessel-volumeofhemisphere$

= $\pi \times 7^2\times 16-\frac{2}{3}\times \pi 7^3$
= [ $\pi \times 7^2\left]\right[16-\frac{14}{3})$ ]
=[$\frac{22}{7}\times 7^2$] [$\frac{48-14}{3}$] = [$\frac{22\times 7\times 34}{3}$]

= $\frac{5236}{3}$

= 1745.33 $c{m}^3$