Question

The diameters of two cones are equal.If their slant heights are in the ratio 5:4,find the ratio of their curved surfaces.

Answer 1

Let diameter of one cone=d

and diameter of second cone=d

$\therefore Radiusofthefirstcone\left(r\right)=\frac{d}{2}andofsecondcone\left(r_2\right)=\frac{d}{2}$

Ratio in their slant heights =5:4

Let slant height of the first cone=5x

Then that of second cone=4x

Now curved surface of the first cone=$\pi rl=\pi \frac{d}{2}\times 5x=\frac{5}{2}\pi dx$

$Curvedsurfaceareaofthesecondcone=\pi \times \frac{d}{2}\times 4x=2\pi dx$

$Nowratiobetweenthem=\frac{5}{2}\pi dx:2\pi dx=5:4$