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.