The volume of a right circular cone is 9856 \({cm}^3\) . If the diameter of the base is 28 cm, find
i) height of the cone
ii) slant height of the cone
iii) curved surface area of the cone.

Given :
Radius of the base = \(\frac{28}{2} cm = 14 cm\)
Also, Volume of a right circular cone = 9856 \({cm}^3\)

i) Let the height of the cone be h.

But, we know that,

Volume of right circular cone = \(\frac{1}{3} {\pi} {r}^2 h\)
\(\Rightarrow \) 9856 \({cm}^3\) = \(\frac{1}{3} × \frac{22}{7} × {14}^2 × h\) \({cm}^2\)
\(\Rightarrow \) h = 48 cm.

Therefore, height of the cone is 48 cm.

ii)We know, slant height of cone
= \(\sqrt({h}^2 + {r}^2)\) cm
= \(\sqrt({48}^2 + {14}^2)\) cm
l = \(50 cm\)

Therefore, slant height of the cone is 50 cm.

iii) We also know that,
Curved surface area of the cone
= \({\pi}rl\)
= \(\frac{22}{7} × 14 × 50 {cm}^2\)
= 2200 \({cm}^2\)

Therefore, the curved surface area of the cone is 2200 \({cm}^2\).