SOLUTION: Please help me with this question, I am having trouble finding the answer: A = 2πr^2 + 2πrh = surface area of steel cylinder Question: Find the required radius of

Algebra ->  Surface-area -> SOLUTION: Please help me with this question, I am having trouble finding the answer: A = 2πr^2 + 2πrh = surface area of steel cylinder Question: Find the required radius of       Log On


   

Question 1066747: Please help me with this question, I am having trouble finding the answer:
A = 2πr^2 + 2πrh = surface area of steel cylinder
Question:
Find the required radius of A = 125,000mm^2 and h= 150mm.
Thank you in advanced
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A = pi*r^2 + 2pi*r*h = surface area of steel cylinder
---
Find the required radius of A = 125,000mm^2 and h= 150mm.
-------
That's the lateral area and one end.
A = pi*r^2 + 2pi*r*h = 125000
pi*r^2 + 2pi*r*150 = 125000
r^2 + 300r - 125000/pi = 0
-----------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B300x%2B-39788.7357729738+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28300%29%5E2-4%2A1%2A-39788.7357729738=249154.943091895.

Discriminant d=249154.943091895 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-300%2B-sqrt%28+249154.943091895+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28300%29%2Bsqrt%28+249154.943091895+%29%29%2F2%5C1+=+99.5771138806076
x%5B2%5D+=+%28-%28300%29-sqrt%28+249154.943091895+%29%29%2F2%5C1+=+-399.577113880608

Quadratic expression 1x%5E2%2B300x%2B-39788.7357729738 can be factored:
1x%5E2%2B300x%2B-39788.7357729738+=+%28x-99.5771138806076%29%2A%28x--399.577113880608%29
Again, the answer is: 99.5771138806076, -399.577113880608. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B300%2Ax%2B-39788.7357729738+%29

===============
r =~ 99.577 mm
Ignore the negative solution.