If the radius of a cylinder is doubled while the height remains the same, the volume changes by a factor of:

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Prepare for the NES Elementary Education Test with flashcards and multiple-choice questions. Each question comes with hints and explanations to enhance your learning. Get ready for your exam!

Multiple Choice

If the radius of a cylinder is doubled while the height remains the same, the volume changes by a factor of:

Explanation:
Volume of a cylinder is determined by V = π r^2 h, so the height stays the same while the radius changes the base area. If the radius doubles, the base area becomes π (2r)^2 = 4πr^2, making the volume four times larger: V' = 4V. So the volume changes by a factor of four. Doubling the radius would give a factor of two only if the relationship were linear with r, which it isn’t because the radius is squared. An eightfold change would require tripling the radius, and a factor of one would mean no change.

Volume of a cylinder is determined by V = π r^2 h, so the height stays the same while the radius changes the base area. If the radius doubles, the base area becomes π (2r)^2 = 4πr^2, making the volume four times larger: V' = 4V. So the volume changes by a factor of four. Doubling the radius would give a factor of two only if the relationship were linear with r, which it isn’t because the radius is squared. An eightfold change would require tripling the radius, and a factor of one would mean no change.

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