A right circular cone of radius 20 cm has its volume 8800 cm³. Find its:

(a) height

(b) curved surface area.

Give your answer to the nearest whole number.

Let height of cone be h cm.

Given,

Radius of cone (r) = 20 cm

(a) Given,

Volume = 8800 cm³

By formula,

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

∴ $\dfrac{1}{3}\pi r^2 h = 8800$

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

Hence, height of cone = 21 cm.

(b) By formula,

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

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

By formula,

Curved Surface Area of cone = πrl

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

⇒ $\dfrac{12760}{7}$

⇒ 1822.857 ≈ 1823 cm².

Hence, curved surface area of cone = 1823 cm².