Question

The inner diameter of a glass is $7cm$ and it has raised portion in the bottom in the shape of a hemisphere as shown in the figure. If the height of the glass is $16cm$, find the apparent capacity and the actual capacity of the glass, $(Take\pi =\frac{22}{7})$

Answer 1

Given the inner diameter of the glass $=7cm$
So, the radius of the glass
$r=\frac{7}{2}=3.5cm$
Height of the glass $=16cm$
The volume of the cylindrical glass $=\pi r^{2}h$
$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 16$
$=616c{m}^3$
Now, radius of the hemisphere = Radius of the cylinder
$=r=3.5cm$
Volume of the hemisphere $=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 3.5$
$=89.83c{m}^3$
Now,
Apparent capacity of the glass = Volume of cylinder $=616c{m}^3$
The actual capacity of the glass
= Total volume of cylinder - Volume of hemisphere
$=616-89.83$
$=526.17c{m}^3$
Hence,
Apparent capacity of the glass $=616c{m}^3$
and actual capacity of the glass $=526.17c{m}^3$