Question

The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone.$\left(\mathrm{\pi }=\frac{22}{7}\right)$

Answer 1

Let the radius of the base of the cone be r cm.

Slant height of the cone, l = 50 cm

Curved surface area of the cone = 2200 cm²

∴ $\mathrm{\pi }$rl = 2200 cm²

$$\begin{gathered} \Rightarrow \frac{22}{7}\times r\times 50=2200 \\ \Rightarrow r=\frac{2200\times 7}{22\times 50}=14\mathrm{cm} \end{gathered}$$
∴ Total surface of the cone = $\mathrm{\pi }$r(r + l) = $\frac{22}{7}\times 14\times \left(14+50\right)=\frac{22}{7}\times 14\times 64$ = 2816 cm²

Thus, the total surface area of the cone is 2816 cm².