A cone and a cylinder have the same base radius and height. How do their volumes

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Question: A cone and a cylinder have the same base radius and height. How do their volumes compare?

Options:

Correct Answer: Cone has half the volume of the cylinder

Solution:

Volume of cone = (1/3)πr²h; Volume of cylinder = πr²h. Therefore, cone\'s volume is one-third of the cylinder\'s volume.

A cone and a cylinder have the same base radius and height. How do their volumes compare?

A cone and a cylinder have the same base radius and height. How do their volumes compare?

Step 1: Understand that both the cone and the cylinder have the same base radius (r) and height (h).
Step 2: Write down the formula for the volume of a cone: Volume of cone = (1/3)πr²h.
Step 3: Write down the formula for the volume of a cylinder: Volume of cylinder = πr²h.
Step 4: Compare the two volumes: The volume of the cone is (1/3) of the volume of the cylinder.
Step 5: Conclude that the volume of the cone is one-third of the volume of the cylinder.

Volume of Solids – Understanding the formulas for calculating the volumes of cones and cylinders.
Comparison of Volumes – Analyzing how the volumes of different geometric shapes relate to each other when they share dimensions.