#### Questions

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 1

It can be observed that the radius of the conical part and the hemispherical part is same (i.e., 3.5 cm).

Height of hemispherical part = Radius (r) = 3.5 = 7/2 cm

Height of conical part (h) = 15.5 − 3.5 = 12 cm

#### Solution 2

We have to find the total surface area of a toy which is a cone surmounted on a hemisphere.

Radius of hemisphere and the base of the cone (r) = 3.5cm

Height of the cone,

h = 15.5 - 3.5 = 12 cm

slant height (l) = `sqrt(h^2 + r^2)`

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

`= sqrt(156.25)`

= 12.5 cm

So total surface are of toy

S = πrl + 2πr^{2}

= πr(l + 2r)

`= 22/7 xx 3.5 (12.5 + 2 xx 3.5)`

= 214.5 cm^{2}