rearrange A = 2 pi r (r+h) to make h the subject
(cylinder)
A = 2 pi r (r+h)
A = 2π r^2 + 2πrh
A - 2πr^2 = 2πrh
h = (A - 2πr^2)/(2πr)
To rearrange the formula A = 2πr(r+h) to make h the subject, we need to isolate the variable h.
Step 1: Expand the formula
A = 2πr(r+h)
A = 2πr^2 + 2πrh
Step 2: Move the term 2πr^2 to the other side of the equation
2πr^2 = A - 2πrh
Step 3: Divide both sides of the equation by 2πr
2πr^2 / (2πr) = (A - 2πrh) / (2πr)
Simplifying:
r = (A - 2πrh) / (2πr)
Step 4: Multiply both sides of the equation by (2πr)
r * (2πr) = (A - 2πrh)
Simplifying:
2πr^2 = A - 2πrh
Step 5: Add 2πrh to both sides of the equation
2πrh + 2πrh = A
Simplifying:
4πrh = A
Step 6: Divide both sides of the equation by 4πr
4πrh / (4πr) = A / (4πr)
Simplifying:
h = A / (4πr)
Therefore, h = A / (4πr)
To rearrange the equation A = 2πr(r + h) to make h the subject, follow these steps:
Step 1: Expand the equation.
A = 2πr² + 2πrh
Step 2: Move the term with h to one side of the equation.
A - 2πr² = 2πrh
Step 3: Divide both sides of the equation by 2πr to isolate h.
(A - 2πr²) / (2πr) = h
Now h is the subject of the equation.