Question

given the formula: A=2πr^2+2πrh , solve for h in terms of A, r and π

Answer 1

2πr^2 + 2πrh = A, divide by 2π

r^2 + hr = A/(2π), add (h/2)^2 to both sides to complete square

r^2 + hr + (h/2)^2 = A/(2π) + (h/2)^2

(r + h/2)^2 = A/(2π) + (h/2)^2, take square root

r + h/2 = sqrt(A/(2π) + (h/2)^2)

r = -h/2 + sqrt(A/(2π) + (h/2)^2)

Answer 2

\[2πr^2+2πrh=A\]\[2πr(r+h)=A\]\[r+h=\frac{A}{2πr}\]\[h=\]