Exploring Volume Formulas: Cylinders vs. Cones

The video tutorial demonstrates a comparison between the volumes of cylinders and cones. Using popcorn kernels, the instructor shows that a cylinder with the same height and base area as a cone can fill exactly three cones. This leads to the derivation of the formula for the volume of a cone as one-third of the volume of a cylinder. The video concludes with a thank you to student volunteers.

What was used to compare the volumes of the cylinder and the cone?

• Water

• Popcorn kernels

• Sand

• Marbles

Tags

CCSS.3.MD.A.2

What characteristic was the same for both the cylinder and the cone?

• Weight

• Color

• Volume

• Height and diameter of the base

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CCSS.1.G.A.1

CCSS.2.G.A.1

Why was it important that the height and the size of the base circle were the same for both the cylinder and the cone?

• To ensure accurate volume comparison

• To make the experiment more visually appealing

• Because different sizes would not fit together

• To use less popcorn kernels

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What was the purpose of using popcorn kernels in the experiment?

• As a measurable substance to compare volumes

• To eat after the experiment

• To make the experiment fun

• Because popcorn is lighter than water

Tags

CCSS.3.MD.A.2

How many cones were filled with popcorn from the cylinder?

• Five

• Four

• Three

• Two

Tags

CCSS.3.MD.A.2

What does the experiment demonstrate about the volume of the cylinder compared to the cone?

• The cylinder has three times the volume of the cone.

• The cylinder has twice the volume of the cone.

• The cylinder and cone have the same volume.

• The cylinder has half the volume of the cone.

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a cylinder?

• 2π * r^2 * h

• 1/3 * π * r^2 * h

• π * r * h

• π * r^2 * h

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

After filling how many cones did the cylinder still have popcorn left?

• After four cones

• After one cone

• After two cones

• It was empty after three cones

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CCSS.3.MD.A.2

What does the experiment suggest about the relationship between the volumes of cylinders and cones?

• Cones hold more volume than cylinders.

• Cylinders hold more volume than cones.

• The volume cannot be compared.

• Cylinders and cones hold the same volume.

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CCSS.5.MD.C.5C

Based on the experiment, what is the formula for the volume of a cone?

• π * r^3 * h

• 1/3 * π * r^2 * h

• 1/3 * π * r * h

• π * r^2 * h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3