The formula for the volume and surface area of a cylinder are based on its radius \( r \) and height \( h \):

### Volume of a Cylinder:
\[
V = \pi r^2 h
\]
Where:
- \( V \) is the volume
- \( r \) is the radius of the base
- \( h \) is the height
- \( \pi \) is approximately 3.14159

### Surface Area of a Cylinder:
The surface area includes the lateral surface and the two circular bases.

\[
A = 2\pi r h + 2\pi r^2
\]
Where:
- \( A \) is the total surface area
- \( 2\pi r h \) is the lateral surface area
- \( 2\pi r^2 \) is the area of the two circular bases

Would you like more details on how these formulas are derived or applied? 

Here are five questions to expand your understanding:
1. How does the volume formula change if the height of the cylinder doubles?
2. What happens to the surface area if you increase the radius by a factor of 2?
3. Can you apply these formulas to find the volume and surface area of a cylinder with a height of 10 cm and a radius of 3 cm?
4. What is the lateral surface area, and how does it differ from the total surface area of the cylinder?
5. How does the volume formula compare to that of a cone or a sphere?

**Tip:** Always ensure units are consistent when calculating volume or surface area.

Explore the key formulas for calculating the volume and surface area of a cylinder, essential concepts in geometry. This page offers a detailed breakdown of the formulas and example questions, suitable for students in Grades 6-8.

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