Question

Find the capacity in litres of a conical vessel with:

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm.

Answer 1

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

Volume =

(i) In a cone, the base radius ‘r’ is given as 7 cm and the slant height ‘l’ is given as 25 cm.

To find the base vertical height ‘h’ we use the relation between r, l and h.

We know that in a cone

=

=

=

= 24

Therefore the vertical height is, h = 24 cm.

Substituting the values of r = 7 cm and h = 24 cm in the above equation and using

Volume =

= (22) (7) (8)

= 1232

Hence the volume of the given cone with the specified dimensions is

(ii) In a cone, the vertical height ‘h’ is given as 12 cm and the slant height ‘l’ is given as 13 cm.

To find the base radius ‘r’ we use the relation between r, l and h.

We know that in a cone

=

=

=

= 5

Therefore the base radius is, r = 5 cm.

Substituting the values of r = 5 cm and h = 12 cm in the above equation and using

Volume =

= 314.28

Hence the volume of the given cone with the specified dimensions is