The Cylinder Volume Formula

Find out how much space is inside any cylinder!

What is a Cylinder? (For Everyone!)

Think about a can of soup, a glass of water, or a paper towel roll. These are all cylinders! A cylinder is a 3D shape with two identical flat ends that are circles and one curved side. Volume is the amount of space inside the cylinder. It's like asking, "How much soup can fit in the can?"

The Cylinder Volume Formula

To find the volume of any cylinder, you only need to know two things: its radius and its height. The formula is:

$$ V = \pi r^2 h $$

Let's break that down:

V stands for the Volume.
π (pi) is a special number, approximately 3.14159.
r is the radius of the circular base. The radius is the distance from the center of the circle to its edge.
h is the height of the cylinder.

The first part of the formula, $ \pi r^2 $, is actually the formula for the area of the circular base. So, another way to think about the volume is: (Area of Base) × Height.

Example: Calculating the Volume

Let's find the volume of a can with a radius (r) of 4 cm and a height (h) of 10 cm.

We use the formula: $ V = \pi r^2 h $

Plug in the values: $ V = \pi \times (4)^2 \times 10 $
Calculate the square of the radius: $ 4^2 = 16 $
Now the formula is: $ V = \pi \times 16 \times 10 $
Multiply the numbers: $ V = 160 \pi $
Multiply by π (approx. 3.14): $ V \approx 160 \times 3.14159 \approx 502.65 $

So, the volume of the can is about 502.65 cubic cm. We use "cubic" units for volume because it's a 3D space.