The curved surface area of a cone of height 8 m is `188.4 m^(2)`. Find the volume of cone.

Explanation

`pi rl=188.4`
`rArr rl=(188.4)/(3.14)=60`
`rArr r^(2)l^(2)=3600`
`rArr r^(2)(h^(2)+r^(2))=3600`
`rArr r^(2)(64+r^(2))=3600`
`rArr r^(4)+64 r^(2)-3600 =0`
`rArr (r^(2)+100) (r^(2)-36) = 0`
`therefore r^(2)=-100` or `r^(2)=36 rArr r = 6` (`because r^(2) = -100` is nor possible)
`therefore` Volume of cone `=(1)/(3)pi r^(2)h`
`=(1)/(3)xx3.14xx36xx8`
`= 301.44 m^(3)`