A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =22/7]

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy

#### Solution

Radius of hemisphere = 3.5 cm

Total height of the toy = 15.5 cm.

Surface area of cone

`=pirl`

`l = sqrt((12)^2 + (3.5)^2)`

`= sqrt156.25`

`=12.5 cm`

Therefore,

Surface area of cone

`= 22/7 xx 3.5 xx 12.5`

`=137.5 cm^2`

Surface area of hemisphere

`=2pir^2`

`= 2 xx 22/7 xx 3.5 xx 3.5`

`= 77 cm^2`

Therefore,

Total surface area of the toy

`=137.5 + 77`

`=214.5 cm^2`

Volume of cone

`=1/3pir^2h`

`=1/3 xx 22/7 xx (3.51^2 xx 12)`

`=154 cm^2`

Volume of hemisphere

`=2/3pir^3`

`= 2/3 xx 22/7 xx (3.5)^3`

`= 89.83 cm `

Therefore,

Total volume of the toy

`= (154 + 89.83) cm^3`

`= 243.83 cm^3`