SOLUTION: Solve the formula for the indicated variable. (Simplify your answer completely.) See Example 4. (Objective 2) A = 2πr2 + 2πhr, for r (The formula for the surface area of a ri

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Solve the formula for the indicated variable. (Simplify your answer completely.) See Example 4. (Objective 2) A = 2πr2 + 2πhr, for r (The formula for the surface area of a ri      Log On


   

Question 1156080: Solve the formula for the indicated variable. (Simplify your answer completely.) See Example 4. (Objective 2)
A = 2πr2 + 2πhr, for r
(The formula for the surface area of a right circular cylinder)
r =

Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
-------------------------------------
A = 2πr2 + 2πhr, solve for r.
-----------------------------------

A=2pi%2Ar%5E2%2B2pi%2Ahr
2pi%2Ar%5E2%2B2pi%2Ahr-A=0
r=%28-2pi%2Ah%2B-+sqrt%284h%5E2%2Api%5E2%2B8pi%2AA%29%29%2F%284pi%29
r=%28-2h%2Api%2B-+2%2Asqrt%28pi%2Ah%5E2%2B2A%2Api%29%29%2F%284pi%29
highlight%28r=%28-h%2Api%2B-+sqrt%28pi%2Ah%5E2%2B2A%2Api%29%29%2F%282pi%29%29
(Look for any mistakes.)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A+=+2pi%2Ar%5E2+%2B+2pi%2Ahr
solve for r
A+=+2pi%28r%5E2+%2B+hr%29
A%2F2pi=r%5E2+%2B+hr.......complete square
A%2F2pi=%28r%5E2+%2B+hr%2Bb%5E2%29-b%5E2.....b=h%2F2
A%2F2pi=%28r%5E2+%2B+hr%2B%28h%2F2%29%5E2%29-%28h%2F2%29%5E2
A%2F2pi=%28r%2Bh%2F2%29%5E2-h%5E2%2F4
A%2F2pi%2Bh%5E2%2F4=%28r%2Bh%2F2%29%5E2
sqrt%28A%2F2pi%2Bh%5E2%2F4%29=r%2Bh%2F2
r=sqrt%28A%2F2pi%2Bh%5E2%2F4%29-h%2F2