A right circular cone of radius 20 cm has its volume 8800 cm 3 . Find its:

Let height of cone be h cm.

Given,

Radius of cone (r) = 20 cm

(a) Given,

Volume = 8800 cm³

By formula,

Volume of cone = $\frac{1}{3}\pi r^2 h$

∴ $\frac{1}{3}\pi r^2 h = 8800$

$$\begin{aligned}\Rightarrow \frac{1}{3} \times \frac{22}{7} \times 20^2 \times h = 8800 \\[1em] \Rightarrow \frac{1}{3} \times \frac{22}{7} \times 400 \times h = 8800 \\[1em] \Rightarrow h = \frac{8800 \times 7 \times 3}{400 \times 22} \\[1em] \Rightarrow h = 7 \times 3 \\[1em] \Rightarrow h = 21 \text{ cm}.\end{aligned}$$

Hence, height of cone = 21 cm.

(b) By formula,

Slant Height of cone (l) = $\sqrt{(r^2 + h^2)}$

$$\begin{aligned}l = \sqrt{(20)^2 + (21)^2} \\[1em] = \sqrt{400 + 441} \\[1em] = \sqrt{841} \\[1em] = 29 \text{ cm}\end{aligned}$$

By formula,

Curved Surface Area of cone = πrl

Curved Surface Area of cone = $\frac{22}{7} \times 20 \times 29$

⇒ $\frac{12760}{7}$

⇒ 1822.857 ≈ 1823 cm².

Hence, curved surface area of cone = 1823 cm².