Question

Curved surface area of a cone is $308c{m}^2$ and its slant height is $14cm$. Find total surface area of the cone.

Answer 1

Step 1: To find the radius

Given that,

Curved surface area of a cone $=$$308c{m}^2$

slant height, $l$$=$$14cm$

We know that,,

Curved surface area of the cone $=\mathrm{\pi }\times \mathrm{r}\times \mathrm{l}$

Therefore,

$\mathrm{\pi }\times \mathrm{r}\times \mathrm{l}$$=308c{m}^2$

$$\begin{gathered} \frac{22}{7}\times r\times 14=308 \\ r=\frac{7\times 308}{22\times 14} \\ r=7cm \end{gathered}$$

Step 2: To find the total surface area

Total surface area of the cone $=curvedsurfacearea+basearea$

Base area of cone

$$\begin{gathered} A=\mathrm{\pi }\times {\mathrm{r}}^2 \\ =\frac{22}{7}\times 7^2 \\ =154{\mathrm{cm}}^2 \end{gathered}$$

Total surface area of the cone $=$ Curved surface area + base area

$=$ $308+154c{m}^2=462c{m}^2$

Hence, the total surface area of the cone is $462c{m}^2$.