Question

Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.

Answer 1

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

Slant height of the cone = 3 × Radius of the cone (Given)

∴ l = 3r

Total surface area of the cone = 616 cm²

∴ $\mathrm{\pi }$r(r + l) = 616 cm²

$$\begin{gathered} \Rightarrow \frac{22}{7}\times r\times \left(r+3r\right)=616 \\ \Rightarrow \frac{22}{7}\times r\times 4r=616 \\ \Rightarrow \frac{88}{7}{r}^2=616 \\ \Rightarrow r^2=\frac{616\times 7}{88}=49 \\ \Rightarrow r=\sqrt{49}=7\mathrm{cm} \end{gathered}$$
∴ Slant height of the cone, l = 3r = 3 × 7 = 21 cm

Thus, the slant height of the cone is 21 cm.