Question

A juice seller was serving his customers using glass. The inner diameter of the cylindrical glass was $5cm$, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was $10cm$, find what the apparent capacity of the glass was and what the actual capacity was (Use $\pi =3.14$)

Answer 1

We have, an inner diameter of the glass $=5cm$, height of the glass $=10cm$

Apparent capacity of the glass $=3.14\times {\left(\frac{5}{2}\right)}^2\times 10{cm}^3=3.14\times \frac{25}{4}\times 10{cm}^3=196.25{cm}^3$

volume of hemispherical part $=\frac{2}{3}\times 3.14\times {\left(\frac{5}{2}\right)}^3{cm}^3=\frac{2}{3}\times 3.14\times 2.5\times 2.5\times 2.5{cm}^3=32.71{cm}^3$

Actual capacity of glass $=$ Apparent capacity of glass - volume of hemispherical part

$=(196.25-32.71){cm}^3$

$=163.54{cm}^3$