The radius and height of a solid right circular cone are in the ratio of 5:12 .If its volume is 314 `cm^(3)` Find its total surface area .`[Take pi =3.14]`

Explanation

Let radius of cone =5x
Height of cone = 12x
`l^(2)=sqrt(169x^(2))=13x`
It is given that volume =`314 cm^(2)`
`(1)/(3)pi(5x)^(2)(12x)=314`
`(1)/(3)xx3.14xx25xx12xxx^(3)=314`
`x^(3)=(314xx3)/(3.14xx25xx12)=1`
x=1cm
Radius r=5`xx`1=5cm
Height h=12`xx`1=12 cm
and slant height l=13`xx`l=13 cm
Now total surface area of cone `=pir(l+r)=3.14xx5(13+5)=3.14xx5xx8`
`=282.60 cm^(2)`
Hence total surface area of cone is 282.60 `cm^(2)`