Question

Find the capacity in litres of a conical vessel with height 12 cm and slant height 13 cm.

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

Answer 1

Height (h) of cone = 12 cm

Slant height (l) of cone = 13 cm

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

= `(sqrt(13^2-12^2))  cm`

= 5 cm

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

= `[1/3xx22/7xx(5)^2xx12]cm^3`

= `(4xx22/7xx25)cm^3`

= `(2200/7)cm^3`

Therefore, the capacity of the conical vessel

= `(2200/7000) "litres"`          ...(1 litre = 1000 cm³)

= `11/35 "litres"`

Answer 2

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

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

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

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

= `sqrt(13^2 - 12^2)`

=` sqrt(169 - 144)`

= `sqrt(25)`

= 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 `pi = 22/7`

Volume = `((22)(5)(5)(12))/((3)(7))`

= 314.28

Hence, the volume of the given cone with the specified dimensions is `314.28  "cm"^3`.