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If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume. - Mathematics

Answer in Brief

If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.

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Solution

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 rl 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)`

= `sqrt(343)`

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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Q 3 | Page 23
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