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.
Solution:
Radius of the hemisphere = Radius of the cone = 7 cm
Height of the cone $=(31-7) \mathrm{cm}=24 \mathrm{~cm}$
Slant height of the cone, $l=\sqrt{r^{2}+h^{2}}$
$=\sqrt{(7)^{2}+(24)^{2}}$
$=\sqrt{49+576}$
$=\sqrt{625}$
$=25 \mathrm{~cm}$
Total surface area of the toy = (Curved surface area of the hemisphere) + (Curved surface area of the cone)
$=2 \pi r^{2}+\pi r l$
$=\pi \times r \times(2 r+l)$
$=\frac{22}{7} \times 7 \times(14+25) \mathrm{cm}^{2}$
$=858 \mathrm{~cm}^{2}$