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 diameter 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 that of second cone=3x

Now, curved surface area of the first cone = $\pi rl=\pi \times \frac{d}{2}\times 4x=2\pi dx$

Curved surface area of second cone = $\pi \times \frac{d}{2}\times 3x=\frac{3}{2}\pi dx$

Now, ratio of their curved surface areas = $2\pi dx:\frac{3}{2}\pi dx=4:3$