Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total
surface area of the toy. [CBSE 2012]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{hemisphere}=\mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cone}=r=3.5\mathrm{cm}\mathrm{and} \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{cone}=15.5-3.5=12\mathrm{cm} \\ \mathrm{Also}, \\ \mathrm{The}\mathrm{slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cone},l=\sqrt{h^2+r^2} \\ =\sqrt{{12}^2+3.5^2} \\ =\sqrt{144+12.25} \\ =\sqrt{156.25} \\ =12.5\mathrm{cm} \\ \mathrm{Now}, \\ \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{toy}=\mathrm{CSA}\mathrm{of}\mathrm{cone}+\mathrm{CSA}\mathrm{of}\mathrm{hemisphere} \\ =\mathrm{\pi }rl+2\mathrm{\pi }{r}^2 \\ =\mathrm{\pi }r\left(l+2r\right) \\ =\frac{22}{7}\times 3.5\times \left(12.5+2\times 3.5\right) \\ =11\times \left(12.5+7\right) \\ =11\times 19.5 \\ =214.5{\mathrm{cm}}^2 \end{gathered}$$

So, the total surface area of the toy is 214.5 cm².

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.