If a cylinder’s radius is doubled and its height is halved, how does the volume change given V = π r^2 h?

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Multiple Choice

If a cylinder’s radius is doubled and its height is halved, how does the volume change given V = π r^2 h?

Explanation:
Doubling the radius makes the base area grow fourfold because the area depends on r^2. Halving the height reduces the height factor by half. So the volume scales by 4 (from the base area) times 1/2 (from the height), which is a net factor of 2. If you substitute the new dimensions into V = π r^2 h, you get V' = π (2r)^2 (h/2) = 4πr^2 · (h/2) = 2πr^2h = 2V. So the volume doubles.

Doubling the radius makes the base area grow fourfold because the area depends on r^2. Halving the height reduces the height factor by half. So the volume scales by 4 (from the base area) times 1/2 (from the height), which is a net factor of 2. If you substitute the new dimensions into V = π r^2 h, you get V' = π (2r)^2 (h/2) = 4πr^2 · (h/2) = 2πr^2h = 2V. So the volume doubles.

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