SOLUTION: A conical paper cup is to have a height of 3 inches. Find the radius r of the cone that will result in a surface area of 6πin^2

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A conical paper cup is to have a height of 3 inches. Find the radius r of the cone that will result in a surface area of 6πin^2      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 906474: A conical paper cup is to have a height of 3 inches. Find the radius r of the cone that will result in a surface area of 6πin^2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Looking for the formula for lateral surface area of a cone in a textbook
or in some other reference is useful.

Lateral Surface Area for a cone, pi%2Ar%2AL, where L=sqrt%28r%5E2%2Bh%5E2%29, the LATERAL height;
and h is the cone's height. You are not interested in any bottom surface contributed by the circular
part opposite the tip(the pointy part) of the cone.

A for the lateral surface area,
Given A=6pi square inches and h=3,
pi%2Ar%2AL=A
pi%2Ar%28sqrt%28r%5E2%2Bh%5E2%29%29=A
r%28sqrt%28r%5E2%2Bh%5E2%29%29=A%2Fpi
r%5E2%28r%5E2%2Bh%5E2%29=%28A%2Fpi%29%5E2
r%5E4%2Bh%5E2%2Ar%5E2=%28A%2Fpi%29%5E2
r%5E4%2Bh%5E2%2Ar%5E2-%28A%2Fpi%29%5E2=0
This is an equation in quadratic form, so you can solve for r, either symbolically first,
or maybe plug in all the known given values first, and then solve that way. I would
plug in the known values now and solve for r%5E2 and then for r from that. Either way,
these will be lengthy steps.