The curved surface area of a cone is $$308\ cm^{2}$$ and its slant height is $$14\ cm$$. Find the radius of the base and total surface are of the cone.
Consider $$r$$ as the radius of the cone
It is given that
Slant height of the cone $$=14\ cm$$
Curved surface area of the cone $$=308\ cm^{2}$$
It can be written as
$$\pi rl=308$$
By substituting the values
$$\dfrac{22}{7}\times r\times 14=308$$
On further calculation
$$22\times r\times 2=308$$
So we get
$$r=\dfrac{308}22\times 2)$$
$$r=7\ cm$$
We know that
Total surface area of a cone $$=\pi rl(1+r)$$
By substituting the values
Total surface area of cone $$=\dfrac{22}{7}\times 7\times (14+7)$$
On further calculation
Total surface area of a cone $$=22\times 21=462\ cm^{2}$$
Therefore, the base radius of the cone is $$7\ cm$$ and the total surface area is $$462\ cm^{2}$$