The volume of a right circular cone is `9856` `c m^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.

Explanation

We have, `V = 9856 cm^(3) and r = 14 cm`
(i) Let the height of the cone be `h cm`
Then, volume `= (1)/(3) pi r^(2)h`
`rArr 9856 = (1)/(3) xx (22)/(7) xx 14 xx 14 xx h`
`rArr h = ((9856 xx 3 xx 7)/(22 xx 14 xx 14)) = 48`
`:.` height of the cone is `48 cm`
(ii) Let the slant height of the cone be `l` cm. Then,
`l^(2) = r^(2) + h^(2)`
`rArr l^(2) = (14)^(2) + (48)^(2) = 196 + 2304 = 2500`
`rArr l = sqrt(2500)= 50`
`:.` height of the cone is `50 cm`
(iii) Curved surface area of the cone
`= pi rl`
`= ((22)/(7) xx 14 xx 50) cm^(2) = 2200 cm^(2)`
`:.` curved surface area of the cone is `2200 cm^(2)`