The Lesson
The volume of a cylinder is found using the formula:

In this formula,
r is the
radius of the cylinder and
h is the height of the cylinder. The image below shows what we mean by the radius and height:

"Find the Volume" Widget
Here is a widget to help you learn the formulas to find the volumes of different shapes.
- Click on the shape you're learning about.
- Click on the pad to start.
- Follow the instructions in the bottom-left corner.
- On the last click, the formula, workings, and answer will appear in the yellow box.
- Good luck!
How to Find the Volume of a Cylinder
What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm, as shown below?
Step-by-Step:
1
Start with the formula:
Volume = πr2h
Don't forget: π is
pi (≈ 3.14)
and r
2 = r × r (r
squared).
2
Substitute the radius and the height into the formula. In our example, r = 5 and h = 10.
Volume = π × 52 × 10
Volume = π × 5 × 5 × 10
Volume = π × 250
Volume = 3.14 × 250
Volume = 785 cm3
Answer:
The volume of the cylinder with a radius of 5 cm and a height of 10 cm is 785 cm
3.
What Is a Cylinder?
A cylinder has two ends that are circles that are parallel to each other and are joined by a curved surface.
A Sphere in a Cylinder

If a sphere is placed in a cylinder, the
volume of the sphere is exactly two-thirds the volume of the cylinder.
Can you work out why?
A Cone in a Cylinder

If a cone is placed in a cylinder, the
volume of the cone is exactly a third of the volume of the cylinder.
Can you work out why?