Question

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

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone=

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

=

=

=

Therefore the base radius is, r = cm.

Substituting the values of r = cm and h = 21 cm in the formula for volume of a cone.

Volume = $\frac{{\mathrm{\pi r}}^{{}_2}\mathrm{h}}{3}=\frac{\mathrm{\pi }\times {\left(\sqrt{343}\right)}^2\times 21}{3}$
=2401$\mathrm{\pi }$

Hence the volume of the given cone with the specified dimensions is $2401\mathrm{\pi }{\mathrm{cm}}^3$.