Volume of a Cone and Related Concepts

The video tutorial explains how to find the volume of a cone and compares it to a cylinder with the same height and radius, showing that three cones fit into one cylinder. It provides a formula for calculating cone volume and demonstrates it with examples, including finding the height of a cone given its volume. The tutorial emphasizes understanding the formula and solving for missing values.

If a cone and a cylinder have the same height and radius, how many cones are needed to fill the cylinder?

• Four

• Two

• Three

• One

What is the formula for the volume of a cone?

• 1/2 πr²h

• 2πr²h

• 1/3 πr²h

• πr²h

In the example calculation, what is the radius of the cone?

• 5

• 4

• 3

• 2

What is the volume of the cone in the example calculation?

• 70.25 inches³

• 56.52 inches³

• 60.00 inches³

• 45.67 inches³

Given a cone with a volume of 1899.7 cm³ and a radius of 11 cm, what is the height?

• 12 cm

• 15 cm

• 13 cm

• 14 cm

What is the first step in solving for the height in the cone volume formula?

• Square the radius

• Add the height

• Divide by 3

• Multiply by π

What is the result of 11 squared in the height calculation example?

• 100

• 110

• 121

• 130

What operation is used to isolate the height in the cone volume equation?

• Division

• Addition

• Subtraction

• Multiplication

What is the rounded height of the cone in the practical example?

• 15 cm

• 17 cm

• 16 cm

• 14 cm

What should you remember when using the cone volume formula?

• Multiply by 1/3

• Use the diameter instead of radius

• Always multiply by 2

• Ignore the height