mathcounts problem 11

label Mathematics
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schedule 1 Day
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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.

Dec 26th, 2014

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.

Dec 26th, 2014

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