SOLUTION: May you please help me with this question??: If the volume of a right cone is 72p(72 PI, can't put the sign on, srry), find the surface area if its height and radius are equal.

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Question 33541This question is from textbook Addison-Wesley Geometry
: May you please help me with this question??:
If the volume of a right cone is 72p(72 PI, can't put the sign on, srry), find the surface area if its height and radius are equal.
Thank you. This question is from textbook Addison-Wesley Geometry

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's first find the radius of the right circular cone from the given information.
The volume of a right circular cone is given by:
V+=+%281%2F3%29%28pi%29r%5E2h = 72%28pi%29 but since r = h we can rewrite this and simplify it.
%281%2F3%29%28pi%29r%5E3+=+72%28pi%29 Divide both sides bypi and multiply both sides by 3.
r%5E3+=+216 Take the cube-root of both sides.
r+=+6
So the radius, r = 6
The surface (lateral) area of a right circular cone is given by:
S+=+%28pi%29r%2Asqrt%28r%5E2%2Bh%5E2%29 but since r = h, we can rewrite this and simplify it.
S+=+%28pi%29r%2Asqrt%28r%5E2%2Br%5E2%29
S+=+%28pi%29r%2Asqrt%282r%5E2%29
S+=+%28pi%29r%5E2%2Asqrt%282%29 Now substitute r = 6.
S+=+%28pi%296%5E2%2Asqrt%282%29
S+=+36%28pi%29%2Asqrt%282%29 This is the surface area of the cone.