Question

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Answer 1

Radius of the hemisphere = Radius of the cone = 7 cm

Height of the cone = (31 − 7) cm = 24 cm

Slant height of the cone,

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

= `sqrt((7)^2 + (24)^2)`

= `sqrt(49 + 576)`

= `sqrt(625)`

= 25 cm

Total surface area of the toy = (Curved surface area of the hemisphere) + (Curved surface area of the cone)

= 2πr² + πrl

= π × r × (2r + l)

= `22/7 xx 7 xx (14 + 25)  cm^2`

= `22/7 xx 7 xx (39)  cm^2`

= 22 × 39

= 858 cm²

Hence, the total surface area of the toy is 858 cm².