2 cylinders are equal in volume. The radius of one is doubled, and the height of the other cylinder is increased to k times its original height. If 2 new cylinders are in equal in volume, what is the volume of k? I know the answer is 4 but I need help explaining it.

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2 cylinders are equal in volume. The radius of one is doubled, and the height of the other cylinder is increased to k times its original height. If 2 new cylinders are in equal in volume, what is the volume of k? I know the answer is 4 but I need help explaining it.

Mathematics
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Other answers:

\[V_1 = \pi (2r)^2 h\] \[V_2 = \pi (r)^2 \, h(k)\] set \(V_1 = V_2\)

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