The ratio of the slant height and radius of the cone is 7 : 4. If itscurved surface area is `550 cm^(2)`, then find its radius.

Explanation

Let slant height of conce l = 7x
and radius r = 4x
Now, curved surface area of conce `= pi rl`
`= pi(7x)(4x)`
`=(22)/(7)(7x)(4x)`
`=88x^(2)cm^(2)`
Given that, `88x^(2)=550`
`rArr x^(2)=(550)/(88)=(25)/(4)`
`rArr x =(5)/(2)`
Now, radius of cone = `4x=4xx(5)/(2)=10 cm`