# geometry

How do you calculate the lateral and surface areas of a cone whose height is 12 in and whose slant height is 15 in.

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asked by JOY
1. Draw a cross section and you will have a right-angled triangle.
find the missing side which will be the radius of the base of the cone , r should be 9 in
You should have formulas for the surface area of a cone.

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posted by Reiny
2. Could you show me the work for this one.
Thank you

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posted by JOY
3. r^2 + 12^2 = 15^2
r^2 = 225-144 = 81
r = √81 = 9

The surface area is made up of two parts,
the base, which is a circle, πr^2 and
the lateral surface (without the base) which has an area of πrs, where s is the slant height of 15 in

So total area is
πr^2 + πrs
= π(9^2) + π(9)(15)
= .....

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posted by Reiny

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