Question

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

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

Answer 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`

= `sqrt(625 - 49)  cm`

= 24 cm

Volume of conical vessel = `1/3pir^2h`

= `(1/3 xx 22/7 xx (7)^2 xx 24)cm^3`

= (154 × 8) cm³

= 1232 cm³

Therefore, the capacity of the conical vessel

= `(1232/1000) "litres"`        ...(1 litre = 1000 cm³)

= 1.232 litres

Answer 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`