Understanding the Volume of a Cone

The video tutorial explains how to find the volume of a cone using the formula 1/3 πr²h. It compares the volume of a cone to that of a cylinder with the same height and radius, noting that it takes three cones to fill a cylinder. The tutorial provides a step-by-step guide to applying the formula, using a cone with a radius of 6 and a height of 10 as an example. The calculation is simplified to find the volume, resulting in 120π cubic units.

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

• A cone has twice the volume of a cylinder.

• A cone has the same volume as a cylinder.

• A cone has one-third the volume of a cylinder.

• A cone has half the volume of a cylinder.

Which formula represents the volume of a cone?

• 1/3 PI R squared times H

• PI R squared times H

• PI R squared

• 2/3 PI R squared times H

What are the two variables needed to calculate the volume of a cone?

• Diameter and height

• Radius and height

• Circumference and height

• Radius and diameter

If the radius of a cone's base is 6 and the height is 10, what is the area of the base?

• 72 PI

• 12 PI

• 18 PI

• 36 PI

What is the volume of a cone with a base radius of 6 and height of 10?

• 120 PI

• 90 PI

• 60 PI

• 180 PI

What is the simplified form of 36 divided by 3?

• 9

• 12

• 15

• 18

What is the first step in calculating the volume of a cone?

• Multiply the height by the radius

• Calculate the area of the base

• Divide the height by three

• Add the radius and height

How many cones are needed to fill a cylinder with the same radius and height?

• Four cones

• Three cones

• Two cones

• Five cones

What is the unit of measurement for volume?

• Square units

• Linear units

• None of the above

• Cubic units