Question

In the given figure, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.

Answer 1

Radius of the sphere = Radius of the cylinder = Radius of cone = r = 3 cm

Height of the cone, h = 4 cm

Height of the cylinder, H = 40 cm

Let the slant height of the cone be l cm.

$\therefore l=\sqrt{r^2+h^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\mathrm{cm}$

Total area of the toy

= Curved surface area of hemisphere + Curved surface area of cylinder + Curved surface area of cone

$$\begin{gathered} =2\mathrm{\pi }{r}^2+2\mathrm{\pi }rH+\mathrm{\pi }rl \\ =2\mathrm{\pi }\times {\left(3\right)}^2+2\mathrm{\pi }\times 3\times 40+\mathrm{\pi }\times 3\times 5 \\ =18\mathrm{\pi }+240\mathrm{\pi }+15\mathrm{\pi } \\ =273\mathrm{\pi }{\mathrm{cm}}^2 \end{gathered}$$
Thus, the total area of the toy is 273$\mathrm{\pi }$ cm².