Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm

`["Assume "pi=22/7]`

#### Solution 1

Radius (*r*) of cone = 7 cm

Slant height (*l*) of cone = 25 cm

`"Height (h) of cone "=sqrt(l^2-r^2)`

`=(sqrt(25^2-7^2))cm`

= 24 cm

`"Volume of cone "=1/3pir^2h`

`=(1/3xx22/7xx(7)^2xx24)cm^3`

= (154 x 8)cm^{3}

= 1232 cm^{3}

Therefore, capacity of the conical vessel

`= (1232/1000)litres" "("1 litre "=1000cm^3)`

= 1.232 litres

#### Solution 2

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

Volume = `1/3 pi r^2 h`

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

`l^2 = r^2 + h^2`

`h^2 = l^2 - r^2`

`h = sqrt(l^2 - r^2)`

`= sqrt(25^2 - 7^2)`

`= sqrt(625-49)`

` = sqrt(576)`

= 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 ` pi = 22/7`

Volume = `((22)(7)(7)(24))/((3)(7))`

= (22) (7) (8)

= 1232

Hence the volume of the given cone with the specified dimensions is `1232 cm^3`