Volume of Cylinders and Cones

Front

What is the formula for the volume of a cylinder?

Back

V = πr²h

Front

What is the formula for the volume of a cone?

Back

V = \frac{1}{3}πr²h

Front

What is the definition of volume?

Back

The amount of space taken up by a 3D solid.

Front

How many times greater is the volume of a cylinder than a cone with the same diameter and height?

Back

3

Front

Why does the formula for the volume of a cone involve dividing by 3?

Back

Because it takes 3 cones to fill up a cylinder.

Front

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

Back

V = π(5 cm)²(10 cm) = 250π cm³ ≈ 785.4 cm³.

Front

What is the volume of a cone with a radius of 3 cm and a height of 9 cm?

Back

V = \frac{1}{3}π(3 cm)²(9 cm) = 27π cm³ ≈ 84.8 cm³.

Front

If a cylinder has a height of 12 cm and a radius of 4 cm, what is its volume?

Back

V = π(4 cm)²(12 cm) = 192π cm³ ≈ 602.9 cm³.

Front

What is the relationship between the volume of a cylinder and a cone with the same base and height?

Back

The volume of the cylinder is 3 times greater than the volume of the cone.

Front

What units are used to measure volume?

Back

Cubic units, such as cm³, m³, or liters.