Question

The curved surface area of a cone is $$2200\ cm^2$$ and its slant height is $$50\ cm$$. Find the total surface area of cone. ($$\pi =\dfrac{22}{7}$$)

Answer 1

Let the radius of the base of the cone be $$r\ cm$$
Slant height of the cone, $$I=50\ cm$$
Curved surface area of the cone $$=2200\ cm^2$$
$$\therefore \pi r I=2200\ cm^2$$
$$\Rightarrow \dfrac{22}{7} \times r \times 50=2200$$
$$\Rightarrow r=\dfrac{2200 \times 7}{22 \times 50}=14\ cm$$
$$\therefore$$ Total surface of the cone $$=\pi r(r+l)=\dfrac{22}{7} \times 14 \times (14+50)=\dfrac{22}{7} \times 14 \times 64=2816\ cm^2$$
Thus, the total surface area of the cone is $$2816\ cm2$$