Question

The diameter of the two right circular cones are equal if their slant heights are in the ratio 3:4,than what is the ratio of their curved surface area?

Answer 1

Let the ratio of diameters be 3x:4x

So,the ratio of their radii is 3x/2:2x

Ratio of their slant heights is 3x:4x

CSA of cone = πr(r+l)

πr(r+l)/πR(R+L)

r(r+l)/R(R+L)

3x/2(3x/2+3x)/2x(2x+4x)

3x/2(3x+6x/2)/2x(6x)
3x/2(9x/2) / 2x(6x)
27x^2 / 18x^2
27/18
9/6
3/2
The required ratio is 3:2 ...