1.

The volume of a right circular cone is 9856 `c m^3`. Ifthe diameter of the base is 28cm, find:(i)height of the cone (ii) slant height of the cone(iii)curved surface area of thecone.

Answer» 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)`


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