Find the capacity in litres of a conical vessel with height 12 cm, slant height 13 cm
`["Assume "pi=22/7]`
Solution 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, capacity of the conical vessel
`=(2200/7000)litres" "("1 litre "=1000cm^3)`
`=11/35 "litres"`
Solution 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`
