The height of a cone is 21 cm and its slant height is 28 cm. The volume of the cone is

Explanation

We have, `h = 21 cm and l = 28 cm`
`:. l^(2) = r^(2) + h^(2) rArr r = sqrt(l^(2) - h^(2)) = sqrt((28)^(2) - (21)^(2)) cm`
`rArr r = sqrt((28 + 21) xx (28 - 21)) cm = sqrt(49 xx 7) cm`
`= 7 sqrt7 cm`
Volume of the cone `= (1)/(3) pi r^(2) h`
`= {(1)/(3) xx (22)/(7) xx (7 sqrt7)^(2) xx 21} cm^(3)`
`= (22 xx 343) cm^(3) = 7546 cm^(3)`