The surface area of a cylinder A is given by A = 2πr 2 + 2πrℎ, where r is radius and h is height. Solve for h.

To solve for \( h \) from the surface area equation of a cylinder:

\[
A = 2\pi r^2 + 2\pi r h
\]

Step-by-step solution:

1. Subtract \( 2\pi r^2 \) from both sides to isolate the term with \( h \):
   \[
   A - 2\pi r^2 = 2\pi r h
   \]

2. Divide both sides by \( 2\pi r \) to solve for \( h \):
   \[
   h = \frac{A - 2\pi r^2}{2\pi r}
   \]

Thus, the formula for \( h \) in terms of \( A \) and \( r \) is:
\[
h = \frac{A - 2\pi r^2}{2\pi r}
\]

Let me know if you need further details or have any questions!

Here are 5 related questions:
1. What is the volume of a cylinder in terms of \( r \) and \( h \)?
2. How does the surface area formula change if the cylinder is hollow?
3. If \( A = 100 \, \text{cm}^2 \) and \( r = 2 \, \text{cm} \), what is the height \( h \)?
4. How would you modify the surface area formula for a cone instead of a cylinder?
5. How does increasing the radius affect the surface area for a fixed height?

**Tip:** Always pay attention to the units of measurement in problems involving surface area or volume!

The surface area of a cylinder A is given by A = 2πr² + 2πrh, where r is radius and h is height. Solve for h.

Learn how to solve for the height h of a cylinder using the surface area formula A = 2πr² + 2πrh. This problem explores key geometric and algebraic concepts, including the manipulation of formulas to isolate variables. Suitable for students in Grades 8-10.

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