Question

radius and slant height of a solid right circular cone are in Ration 3 ratio 5 if the curved surface area is 65 CM square find its volume

Answer 1

let radius and slant height be 3x and 5x
now, csa of cone =πrl
l=√r^2+h^2
5x=√3x^2+h^2
5x^2-3x^2=h^2
25x^2-9x^2=h^2
16x^2=h^2
or
h=4
now,
csa=πrl
65=22/7*5x*3x
65=22/7*15x^2
x=√91/66
now, radius=3√91/66
volume of cone =1/3πr^2h
v=1/3*22/7*(3√91/66)^2*4
v=28cm^3 ans