Question

A juice seller serves his customers units a glass as shown in the figure. The inner diameter of the cylindrical glass is 5 cm but the bottom of the glass has a hemispherical portion raised, which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity.

Answer 1

Inner diameter of a cylindrical glass = 5 cm
Inner radius of the glass = 2.5 cm
Height of the glass = 10 cm
Apparent capacity of the glass = Volume of cylinder$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 2.5\times 2.5\times 10=196.43{\mathrm{cm}}^3$

Volume of hemisphere at the bottom $=\frac{2}{3}{\mathrm{\pi r}}^3=\frac{22}{7}\times \frac{2}{3}\times 2.5\times 2.5\times 2.5=32.74{\mathrm{cm}}^3$

Actual capacity of the glass

$$\begin{gathered} =\mathrm{Volume}\mathrm{of}\mathrm{cylinder}-\mathrm{Volume}\mathrm{of}\mathrm{hemisphere} \\ =196.43-32.74=163.69{\mathrm{cm}}^3 \end{gathered}$$