Question

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, then find the volume of wood in the toy.

Answer 1

We have,

Radius of the cylinder = Radius of the hemispher = r = 3.5 cm and

Height of the cylinder, h = 10 cm

Now,

Volume of the toy = Volume of the cylinder - Volume of the two hemispheres

`= pi"r"^2"h"-2xx2/3pi"r"^3`

`=pi"r"^2("h" - (4"r")/3)`

`= 22/7xx3.5xx3.5xx(10-(4xx3.5)/(3))`

`=38.5xx(10-14/3)`

`=38.5xx16/3`

`=616/3  "cm"^3`

≈ 205.33 cm³ 

So, the volume of wood in the toy is `616/3` cm³ or 205.33 cm³