Question

A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, then find the height of the toy.

Answer 1

We have,

Base radius of cone = Base radius of hemisphere `= r = 7/2 = 3.5` cm,

As, the volume of cone + Volume of hemisphere = 231

`rArr 1/3 pir^2h + 2/3pir^3 = 231`

`rArr 1/3 pir^2 (h + 2r) = 231`

`rArr 1/3 xx 22/7xx3.5xx3.5xx(h + 2xx 3.5) = 231`

`rArr 38.5/3 xx (h + 7) =231`

`rArr h + 7 = 231xx3/38.5`

`rArr h +7 = 18`

` rArr h = 18-7`

`rArr h=11 cm`

so, the hieght of the toy = h + r = 11 + 3.5 = 14.5 cm