Question:
The diameters of two cones are equal. If their slant height are in the ratio 5:4, find the ratio of their curved surfaces.
Solution:
It is given that
Diameters of two cones are equal
Therefore their radius are also equal i.e
r1 = r2
Let the ratio of slant height be x
Therefore l1 = 5x
l2 = 4x
Therefore Ratio of curved surface area = c1/c2
$\Rightarrow c_{1} / c_{2}=\pi r_{1} l_{1} / \pi r_{2} l_{2}$
$=\frac{\pi r_{1} * 5 x}{\pi r_{2} * 4 x}$
= 5/4
∴ Ratio of curved surface area is 5: 4.