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.
Solution:
We have to find the total surface area of a toy which is a cone surmounted on a hemisphere.
Radius of hemisphere and the base of the cone $(r)=3.5 \mathrm{~cm}$
Height of the cone,
h = 15.5 − 3.5 = 12 cm
slant height $(l)=\sqrt{\mathrm{h}^{2}+\mathrm{r}^{2}}$
$=\sqrt{12^{2}+3.5^{2}}$
$=\sqrt{156.25}$
$=12.5 \mathrm{~cm}$
So, total surface area of toy,
$S=\pi r l+2 \pi r^{2}$
$=\pi r(l+2 r)$
$=\frac{22}{7} \times 3.5(12.5+2 \times 3.5)$
$=214.5 \mathrm{~cm}^{2}$