Two 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 the two new cylinders are equal in volume, what is the value of k.
The height has to be increased by 4.
V = pi * r^2 * h
If we plug in 2r for r (because the radius doubled), then we get:
V = pi * (2r)^2 * h
V = pi * 4r^2 * h
This is the same as writing:
V = pi * r^2 * (4h)
Therefore, the height is multiplied by 4.
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