Question

The area of the circular base of a cone is 616 cm² and its height is 48 cm. Find its whose surface area.

Answer 1

Area of circular base = 616 cm²
Therefore,
$$\begin{gathered} \pi r^2=616 \\ \Rightarrow \frac{22}{7}{r}^2=616 \\ \Rightarrow r^2=\frac{616\times 7}{22} \\ \Rightarrow r^2=196 \\ \Rightarrow r=14\mathrm{cm} \end{gathered}$$

And h = 48 cm
Then slant height, l = $\sqrt{r^2+h^2}=\sqrt{{14}^2+{48}^2}=\sqrt{196+2304}=\sqrt{2500}=50\mathrm{cm}$
Total surface are of cone = $\mathrm{\pi r}\left(\mathrm{r}+\mathrm{l}\right)=\frac{22}{7}\times 14\times \left(14+50\right)$

$$\begin{gathered} =\frac{22}{7}\times 14\times 64 \\ =2816{\mathrm{cm}}^2 \end{gathered}$$