height of cylinder is 6 inches. surface area is A=2pi^2+2pirh

The formula for the surface area \( A \) of a cylinder is typically written as:

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

where:
- \( r \) is the radius of the cylinder's base,
- \( h \) is the height of the cylinder,
- \( 2\pi r^2 \) represents the area of the two circular bases, and
- \( 2\pi rh \) represents the lateral surface area of the cylinder.

Given that the height \( h \) is 6 inches, the formula simplifies to:

\[
A = 2\pi r^2 + 2\pi r(6)
\]
\[
A = 2\pi r^2 + 12\pi r
\]

To proceed further, we need the radius \( r \) to find the exact surface area.

Would you like to continue with this, or do you have additional details to provide?

Here are 5 related questions to expand on this topic:

1. What is the volume formula for a cylinder?
2. How do changes in height affect the surface area of a cylinder?
3. How does the surface area of a cylinder compare to a sphere of the same radius?
4. If the height and radius were both doubled, how would that affect the surface area?
5. Can you derive the lateral surface area of a cylinder?

**Tip:** Always ensure the units for radius and height are consistent when calculating surface area or volume.

Learn how to calculate the surface area of a cylinder with a height of 6 inches using the formula A = 2πr^2 + 2πrh. This problem covers key geometry concepts and is suitable for students in Grades 7-10.

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