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.

Answer 1

Given that the diameter of the common base of the cone and hemisphere is 7 cm.
∴ Radius of the cone (r ) = 7 cm
The total height of the toy is 31 cm.

∴
The height of the cone (h) = 31 - 7 = 24 cm
Surface area of the hemisphere = $2{\mathrm{\pi r}}^2$
= $\left(2\times \frac{22}{7}\times 7\times 7\right)$ = 308 cm²
Slant height of the cone (l) = $\sqrt{r^2+h^2}=\sqrt{{\left(7\right)}^2+{\left(24\right)}^2}=\sqrt{625}$ = 25 cm

∴ Curved surface area of the cone = $\mathrm{\pi rl}=\left(\frac{22}{7}\times 7\times 25\right)$ = 550 cm²
Hence,
Total surface area of the toy = Surface area of the hemisphere + Curved surface area of the cone
= (308 + 550) cm²= 858 cm²