Question

problem 1
cylinders a, b, and c have the same radius but different heights.
order the cylinders from least volume to greatest volume.
least volume
cylinder b
cylinder a
cylinder c
greatest volume

Explanation:

The volume of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height. Since the cylinders have the same radius (as indicated by the same base size in the diagram), the volume depends directly on the height. The taller the cylinder, the greater its volume.

Step 1: Analyze the heights of the cylinders

From the diagram, we can observe the heights of the cylinders:

• Cylinder B has the shortest height.
• Cylinder A has a moderate height.
• Cylinder C has the tallest height.

Step 2: Relate height to volume

Since the volume of a cylinder \( V = \pi r^2 h \) and \( r \) is constant for all three cylinders, the volume is directly proportional to the height \( h \). So, a shorter height means a smaller volume, and a taller height means a larger volume.

Step 3: Order the volumes

Based on the heights:

• Least volume: Cylinder B (shortest height)
• Middle volume: Cylinder A (moderate height)
• Greatest volume: Cylinder C (tallest height)

Answer:

Least Volume: Cylinder B
Middle Volume: Cylinder A
Greatest Volume: Cylinder C

(So the order from least to greatest volume is: Cylinder B, Cylinder A, Cylinder C)