Posted by **JOY** on Thursday, May 12, 2011 at 6:29am.

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

- geometry -
**Reiny**, Thursday, May 12, 2011 at 7:16am
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.

- geometry -
**JOY**, Thursday, May 12, 2011 at 7:49am
Could you show me the work for this one.

Thank you

- geometry -
**Reiny**, Thursday, May 12, 2011 at 8:24am
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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