The slant height of a cone is `13 cm` and its total surface area is `90pi cm^(2)`. Find its radius of base.

Explanation

Here, `l = 13 cm`
Now, the total surface area of conce `=90pi`
`rArr pi r(l+r)=90 pi`
`rArr r(13+r)=90`
`rArr r^(2)=13r-90=0`
`rArr r^(2)=18r-5r-90 =0`
`rArr r(r+18)-5(r+18)=0`
`rArr (r+18) (r-5)=0`
`rArr r+18=0` or`r -5=0`
`rArr r=-18` or `r = 5`
But r cannot be negative
`therefore r = 5 cm`