Question

Volume of a cone is 1212 cm³ and its height is 24 cm. Find the surface area of the cone.($\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Let the radius of the base and slant height of the cone be r cm and l cm, respectively.

Height of the cone, h = 24 cm

Volume of the cone = 1212 cm³

$$\begin{gathered} \therefore \frac{1}{3}\mathrm{\pi }{r}^{2}h=1212{\mathrm{cm}}^3 \\ \Rightarrow \frac{1}{3}\times \frac{22}{7}\times r^2\times 24=1212 \\ \Rightarrow r^2=\frac{1212\times 7}{22\times 8}=48.2 \\ \Rightarrow r=7\mathrm{cm}\left(\mathrm{Approx}\right) \end{gathered}$$
Now,

$$\begin{gathered} l^2=r^2+h^2 \\ \Rightarrow l^2={\left(7\right)}^2+{\left(24\right)}^2 \\ \Rightarrow l^2=49+576=625 \\ \Rightarrow l=\sqrt{625}=25\mathrm{cm}\left(\mathrm{Approx}\right) \end{gathered}$$
∴ Surface area of the cone = $\mathrm{\pi }$rl = $\frac{22}{7}\times 7\times 25$ = 550 cm² (Approx)

Thus, the surface area of the cone is approximately 550 cm².