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

Given:

The diameters of two cones are equal.

Their slant heights are in the ratio $5 : 4$.

To do:

We have to find the ratio of their curved surfaces.

Solution:

Let the diameters of each cone be $d$

This implies,

Radius of each cone $(r) =\frac{d}{2}$

Ratio of the slant heights of the cones $= 5:4$

Let the slant height of the first cone be $5x$ and that of the second cone be $4x$.

Therefore,

Curved surface area of the first cone $= 2\pi rh_1$

$=2 \pi \frac{d}{2} \times 5 x$

$=5 \pi d x$

Curved surface area of the second cone $=2 \pi \times \frac{d}{2} \times 4 x$

$=4 \pi d x$

Ratio of their curved surfaces $=5 \pi d x: 4 \pi d x$

$=5: 4$

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