If the whole surface area of a right circular cone be 3696 sq-cm and the ratio of its radius of base and height be `3:4` , then what will be the curved surface area of the cone ?

Explanation

The ratio of the radius of base and hight of the cone is `3:4` , then let the radius of the cone be `3xcm` and height be `4xcm`.
So, the slant height of the cone `=sqrt((3x)^2+(4x)^2)cm=sqrt(25x^2)cm=5x cm`.
The whole surface area of the cone `=3996` sq-cm.
`therefore (22)/(7)xx3xxx(3x+5x)=3696 or , (22)/(7)xx3x xx 8x =3696 or , x^2=(3696xx7)/(22xx3xx8) or , x^2=49 or , x = sqrt(49)=7`.
So, the radius of base of the cone `3x cm =3xx7cm=21cm`
and slant height of the cone `=5x cm = 5xx7 cm = 35 cm`
`therefore` Curved surface area of the cone `= (22)/(7)xx21xx35` sq-cm `=2310` sq-cm.
Hence the required curved surface of the right circular cone `=2310 ` sq-cm.
`therefore` Curved surface surface of the right circular cone `=2310sq-cm`.