Understanding the Volume of a Cone and Cylinder

The video tutorial demonstrates that the volume of a cone is one-third that of a cylinder with the same base and height. The instructor explains the mathematical formula for the volume of both shapes and calculates the volumes using given measurements. A practical demonstration is conducted by filling a cone and a cylinder with water to visually prove the mathematical concept. The video concludes by summarizing the findings and encouraging viewers to subscribe for more math content.

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

• The volume of a cone is twice the volume of a cylinder.

• The volume of a cone is one-third the volume of a cylinder.

• The volume of a cone is half the volume of a cylinder.

• The volume of a cone is equal to the volume of a cylinder.

Which formula represents the volume of a cylinder?

• 1/2 × π × radius² × height

• π × diameter² × height

• π × radius² × height

• 1/3 × π × radius² × height

If the radius of a cylinder is 2.5 cm and the height is 5 cm, what is the volume using π as 3.14?

• 49.0625 cm³

• 98.125 cm³

• 32.7 cm³

• 75.5 cm³

How do you calculate the volume of a cone with a given base and height?

• Multiply the volume of a cylinder by 3

• Divide the volume of a cylinder by 3

• Multiply the volume of a cylinder by 2

• Divide the volume of a cylinder by 2

What is the volume of a cone with a radius of 2.5 cm and height of 5 cm using π as 3.14?

• 75.5 cm³

• 32.7 cm³

• 49.0625 cm³

• 98.125 cm³

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

• Two cones

• Three cones

• Four cones

• One cone

What was the purpose of filling the cone and cylinder with water in the demonstration?

• To show that the cone holds more water than the cylinder

• To visually prove that three cones fill one cylinder

• To demonstrate that the cylinder holds less water than the cone

• To show that the cone and cylinder hold the same amount of water

What is the formula for the volume of a cone?

• 1/2 × π × radius² × height

• 1/3 × π × radius² × height

• π × diameter² × height

• π × radius² × height