How do you solve for R in a=2πR2+2πRh?

2 Answers
Jul 12, 2016

R=h2±h24+a2π

Explanation:

Notice we have a quadratic in R here:

2πR2+2πhRa=0

We can use the quadratic formula:

R=2πh±(2πh)24(2π)(a)4π

R=2πh±4π2h2+8πa4π

R=h2±4π2h2+8πa4π

In the second fraction, we can rewrite the denominator from 4π to 16π2

Our solution becomes:

R=h2±4π2h2+8πa16π2=h2±h24+a2π

Jul 12, 2016

R=2πh±(2πh)2+8πa4π

Explanation:

a=2πR2+2πRh is a quadratic equation in R and can be written as 2πR2+2πRha=0.

We can now solve for R using quadratic formula b±b24ac2a and hence R=2πh±(2πh)2+8πa4π