Question

A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6`  cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm^{2 .}[Use`pi=22/7`]

Answer 1

Let h be the height of the cone and r be the radius of the base of cone.

The volume of the wooden toy = `1/3pir^2h+2/3pir^3`

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

`=1/3xx22/7xx3.5xx3.5(h+7)`

`=77/6(h+7)`

 According to the question,

 `77/6(h+7)=166`

`=>77/6(h+7)=1001/6`

 ⇒h=6

The height of the wooden toy = 6 cm + 3.5 cm  = 9.5 cm

Now,

Curved surface area of the hemispherical part = `2xx22/7xx3.5xx3.5 = 77 cm^2`

 Hence, the cost of painting the hemispherical part of the toy = 77×10  = Rs 770