If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.
The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as
Volume of cone= `1/3 pi r^2 h`
The vertical height is given as ‘h’ = 21 cm, and the slant height is given as ‘l’ = 28 cm.
To find the base radius ‘r’ we use the relation between r, l and h.
We know that in a cone
` l^2 = r^2 + h^2`
`r^2 = l^2 - h^2`
` r= sqrt(l^2 - h^2)`
` = sqrt(28^2 - 21^2)`
=]`sqrt(784 - 441)`
Therefore the base radius is, r = `sqrt(343)` cm.
Substituting the values of r = `sqrt(343)` cm and h = 21 cm in the formula for volume of a cone.
Volume =`(pir^2h)/3 = (pi xx (sqrt343)^2 xx 21)/3`
= 2401` pi`
Hence the volume of the given cone with the specified dimensions is `2401 pi cm^3`.
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