Question

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?

Answer 1

Given height of cone (h) = 4cm

Diameter of cone (d) = 6cm

∴Radius (r) =`6/2 =3 cm`

Let ‘l’ be slant height of cone

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

`=sqrt(3^2+4^2) =5cm`

l = 5cm

∴ Slant height of cone (l) = 5cm.

Curved surface area of cone (S₁) = πrl

S₁ = π(3)(5) = 47.1cm²

Curved surface area of hemisphere (S₂) = 2πr²

`S_2=2pi(3)^2=56.52cm^2`

∴Total surface area(S) = S₁ + S₂

= 47.1 + 56.52

= 103.62cm²

∴ Curved surface area of toy = 103.62cm²