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

REF.Image.

Actual capacity of Glass$=$ Volume of cylinder - Volume of hemisphere

$\Rightarrow$ volume of cylinder$=\pi r^{2}h$

where $r=\frac{D}{2}=\frac{5}{2}cm;$

$h=10cm;D=3.14$

$\Rightarrow 3.14\times (\frac{5}{2}{)}^2\times 10$

$\Rightarrow 3.14\times 6.25\times 10$

$\Rightarrow 196.25c{m}^3$

Volume of Hemisphere $\Rightarrow \frac{2}{3}\pi r^3$

$(r=\frac{5}{2})$

$\Rightarrow \frac{2}{3}\times 3.14\times (\frac{5}{2}{)}^3$

$\Rightarrow \frac{2}{3}\times 3.14\times 15.625$

$\Rightarrow 32.7c{m}^3$

$\therefore$ Actual capacity $196.25-32.7$$=163.55c{m}^3$

and apparent capacity $\Rightarrow 196.25c{m}^3$