To make \(h\) the subject of the formula \(A = 2\pi r(r + h)\), we'll need to solve for \(h\):
Given formula: \(A = 2\pi r(r + h)\)
Step 1: Distribute \(2\pi r\) on the right side:
\(A = 2\pi r^2 + 2\pi r h\)
Step 2: Subtract \(2\pi r^2\) from both sides:
\(A - 2\pi r^2 = 2\pi r h\)
Step 3: Divide both sides by \(2\pi r\):
\(\frac{A - 2\pi r^2}{2\pi r} = h\)
So, the formula for \(h\) in terms of \(A\) and \(r\) is:
\[h = \frac{A - 2\pi r^2}{2\pi r}\]
The option (a) you provided is the correct expression for \(h\) in terms of \(A\), \(r\), and \(pi\).