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

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

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#### 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`

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