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 $4 : 3$.

 Given:

The diameters of the bases of two cones are equal and slant heights are in the ratio $4 : 3$.

To do:

We have to find the ratio of the curved surface areas of the cones.

Solution:

Let the diameters of each cone be $d$.

This implies,

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

Ratio of the slant heights $= 4 : 3$

Let the slant height of the first cone be $4x$ and the slant height of the second cone be $3x$.

Therefore,

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

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

$=4 \pi d x$

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

$=3 \pi d x$

Ratio of the curved surfaces of the cones $=4 \pi d x: 3 \pi d x$

$=4: 3$

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Updated on: 10-Oct-2022

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