Question

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4:3.

Answer 1

Let diameters of each cone =d

Then radius (r)=$\frac{d}{2}$

Ratio in their slant heights=4:3

Let slant height of first cone=4x

and height height of second cone=3x

Now curved surface area of the first cone=2\pi rh \(=2\times \pi \times \frac{d}{2}\times 4x=4 \pi d x\\and~of~second~cone=2\times \pi \times \frac{d}{2}\times 3x =3 \pi dx\\Now~ratio~in~their~curved~surfaces~=4 \pi dx:3 \pi dx=4:3