Question

The inner 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

Given the inner diameter of the glass = 7cm

So, the radius of the glass 

 `"r"=7/2 "cm"` = 3.5 cm

Height of the glass, h = 16 cm and 

The volume of the cylindrical glass = πr²h

= `22/7xx7/2xx7/2xx16`

= 616 cm³

Now, radius of the hemisphere = Radius of the cylinder 

= r = 3.5 cm

Volume of hemisphere = `2/3`πr³

= `2/3xx22/7xx3.5xx3.5xx3.5`

= 89.83cm³

Now, 

Apparent capacity of the glass = Volume of cylinder = 616 cm³

The actual capacity of the glass = Total volume of cylinder - Volume of hemisphere

= 616 - 89.83

= 526.17 cm³

Hence,

Apparent capacity of the glass = 616 cm³

and actual capacity of the glass = 526.17 cm³