Fermat 2005 Q17

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Problem Statement

A cylinder with radius 2 cm and height 8 cm is full of water. A second cylinder of radius 4 cm and height 8 cm is empty. If all of the water is poured from the first cylinder into the second cylinder, the depth of the water in the second cylinder will be

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Solution

$$\text{Cylinder 1: } r = 2, h = 8, V = \pi \times r^2 \times h = 32\pi$$ $$\text{Cylinder 2: } r = 4, h = ?, V = 32\pi$$ $$\pi \times r^2 \times h = 32\pi$$ $$4^2 \times h = 32 \implies h = 2$$