Volume of Cylinders Examples

What is the volume of this cylinder if its circumference is 125.7 feet?

To find the volume, we need to know the radius and the height. Height is given to us, and we can find the radius using the circumference.

C = 2πr
125.7 ft = 2πr

That's all we need. Like Taco Bell's Crunchwrap Supreme, we're good to go.

V = πr²h
V = π(20 ft)²(80 ft)
V ≈ 100,531 ft³

A cube has a cylindrical hole with a diameter of 5 centimeters cut into it all the way through. What is the volume of the shape?

We'll calculate the volume exactly how the shape is formed: finding a cube and cutting a piece of it out. First, we can find the volume of the whole cube (whole, not holed), and then we can subtract the volume of the cylinder.

For a cube, the length, width, and height are all the same.

V_cube = s³ = (10 cm)³ = 1000 cm³

Now we surgically remove the cylinder. Its diameter is 5 cm, meaning the radius is 2.5 cm. The height of the cylinder is the same as the edge of the cube: 10 cm.

V_cylinder = πr²h
V_cylinder = π(2.5 cm)²(10 cm)
V_cylinder = 62.5π ≈ 196.3 cm³

That means our final volume is the cube minus the cylinder.

V_total = V_cube – V_cylinder
V_total = 1000 cm³ – 196.3 cm³
V_total = 803.7 cm³