Question

A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. Determine the surface area of the toy. (Use π = 3.14)

Answer 1

Radius of hemisphere and the cone are the same.
So, r = 3 cm
Surface area of the cone
$$\begin{gathered} =\mathrm{\pi rl} \\ =3.14\times 3\times \sqrt{3^2+4^2} \\ =47.1{\mathrm{cm}}^2 \end{gathered}$$

Surface area of the hemisphere
$$\begin{gathered} =2{\mathrm{\pi r}}^2 \\ =2\times 3.14\times 9 \\ =56.52{\mathrm{cm}}^2 \end{gathered}$$

Total surface area of the toy = Surface area of the cone + surface area of the hemisphere
=47.1 + 56.52 cm²
=103.62 cm²