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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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