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If the height of a cylinder is doubled while keeping the radius constant, how do
If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
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Q1
If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
It remains the same
It doubles
It triples
It quadruples
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Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.
Questions & Step-by-step Solutions
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Q
Q: If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
Solution:
Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.
Steps: 8
Show Steps
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.
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