If the height of a cylinder is doubled while keeping the radius constant, how do

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Question: If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?

Options:

Correct Answer: It doubles

Solution:

Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.

If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?

If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?

Step 1: Understand the formula for the volume of a cylinder, which is Volume = πr²h.
Step 2: Identify the variables in the formula: r is the radius and h is the height.
Step 3: Note that we are keeping the radius (r) constant and only changing the height (h).
Step 4: If the height is doubled, we replace h with 2h in the formula.
Step 5: Substitute 2h into the volume formula: Volume = πr²(2h).
Step 6: Simplify the equation: Volume = 2πr²h.
Step 7: Compare the new volume (2πr²h) with the original volume (πr²h).
Step 8: Conclude that the new volume is double the original volume.

Volume of a Cylinder – Understanding the formula for the volume of a cylinder, which is V = πr²h, and how changes in height and radius affect the volume.
Proportional Relationships – Recognizing how doubling one dimension (height) while keeping another constant (radius) results in a proportional change in volume.