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Sinking Feeling

Age 14 to 16 Short Challenge Level:

The water completely fills the space between the cylinders up to the height of the smaller cylinder, and also half of the smaller cylinder. The volume of a cylinder is $V=\pi r^2h$, so can calculate the total volume of water by adding these two volumes together.

Between the cylinders the volume is:
$$V = \pi[10^2-5^2]\times 16=1200\pi$$
The volume in the smaller cylinder is
$$V = \pi (5^2 \times 8)=200\pi$$
So the total volume is:
$$V= 1200\pi + 200\pi = 1400\pi$$

In the large cylinder without the smaller cylinder, this volume occupies up to a height $h$ that satisfies:

$$100h\pi = 1400\pi \Rightarrow h=14$$
You can find more short problems, arranged by curriculum topic, in our short problems collection.