Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [CBSE 2017]

Answer 1

The radius of hemisphere as well as that of base of cone is r = 3.5 cm.
The height of toy = 15.5 cm.
The height of hemisphere, h = 3.5 cm and height of cone = 15.5$-$3.5 = 12 cm.
Using Pythagoras Theorem, slant height of cone is $l=\sqrt{{\left(3.5\right)}^2+{\left(12\right)}^2}=\sqrt{12.25+144}=\sqrt{156.25}=12.5\mathrm{cm}$.
Therefore, the Total surface area of toy = Curved surface of cone + Curved surface of hemisphere
$$\begin{gathered} =\mathrm{\pi }rl+2\mathrm{\pi }{r}^2=\frac{22}{7}\times 3.5\times 12.5+2\times \frac{22}{7}\times {\left(3.5\right)}^2 \\ =\frac{275}{2}+77=\frac{275+154}{2}=\frac{429}{2}=214.5{\mathrm{cm}}^2. \end{gathered}$$