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

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

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