Question:
Note Use $\pi=\frac{22}{7}$, unless stated otherwise.
The curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
Solution:
Slant height, l = 14 cm
Let the radius of the base be r cm.
Curved surface area of the cone = 308 cm2 (Given)
$\therefore \pi r l=308$
$\Rightarrow \frac{22}{7} \times r \times 14=308$
$\Rightarrow r=\frac{308 \times 7}{22 \times 14}$
$\Rightarrow r=7 \mathrm{~cm}$
$\therefore$ Total surface area of the cone $=\pi r(r+l)=\frac{22}{7} \times 7 \times(7+14)=\frac{22}{7} \times 7 \times 21=462 \mathrm{~cm}^{2}$
Thus, the radius of the base is 7 cm and the total surface area of the cone is 462 cm2.