Solve Surface Area Formula For Radius Ok. I have

siliciooy0j

siliciooy0j

Answered question

2022-03-22

Solve Surface Area Formula For Radius
Ok. I have a Surface Area Formula for a cylinder, but I am wanting to solve for the radius. The only information I have is the height of the cylinder, which is 8 inches. I know I can use the Quadratic Formula to convert the formula to solve for the radius, but I get stuck when doing the math.
SA=2πr2+2πrh

Answer & Explanation

undodaonePvopxl24

undodaonePvopxl24

Beginner2022-03-23Added 13 answers

If you have
A=2πr2+2πrh
then rearrange it: 2πr2+2πhrA=0
This is quadratic in r with solutions:
r=2πh±4π2h2+8πA4π.
Since the expression under the radical is greater than 2πh you choose the "plus" root so that the radius is positive:
r=2πh+4π2h2+8πA4π.
But to solve for the numerical value of r given h=8 inches, you'll need more information. You'll need the surface area also to get the value of r.
Harry Gibson

Harry Gibson

Beginner2022-03-24Added 13 answers

I'd just complete the square:
A=2πr2+2πrh
A2π=r2+rh
To complete the square on the right-hand side, we need to add h24 to both sides:
A2π+h24=r2+rh+h24
A2π+h24=(r+h2)2
Since r>0 and h>0, we take the positive root:
r+h2=A2π+h24
r=h2+A2π+h24

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