The volume of a cylinder is the amount of space it occupies inside, and it's found with the formula V = π × r² × h, where r is the radius of the base and h is the height. You first find the area of the circular base, then multiply it by the height. It's usually learned around 6th grade, once kids already know the area of a circle, and it's the gateway into three-dimensional geometry. This guide explains the cylinder volume formula with worked, step-by-step examples.
What is the volume of a cylinder?
The volume of a cylinder is the amount of space that fits inside this three-dimensional shape. Think of a soda can, a cardboard tube or a drinking glass: all three are cylinders. Volume is measured in cubic units, like cm³ or m³, because now we're talking about a solid body with depth, not a flat surface.
Two ideas are worth telling apart:
- The base area is the surface of the circle that forms the top or bottom of the cylinder.
- The volume is all the space inside the whole cylinder, height included.
To find the volume you need two values: the radius (r) of the circular base and the height (h) of the cylinder. With those two numbers and the number π you can apply the formula. In the next sections we go step by step, first using the radius and then starting from the diameter.
Tip: if your child understands that volume is the base area repeated along the height, they'll stop memorizing the formula. Try a free class and watch them reason with real shapes.
