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Geometry Difficulty 2.7 Junior Find the answer Canada

Two cylinders are standing on a flat table. Cylinder A has radius
$2$ and height $8$ . Cylinder B has radius $8$ and height $2$ . Cylinder A is $\frac{3}{4}$ full of water and Cylinder B
is empty.

If all of the water from Cylinder A is then poured into Cylinder B,
what fraction of Cylinder B is full of water?

(The volume of a cylinder with radius $r$ and height $h$ is $\pi r^2h$ .)

Pick one

Solution

Solution 1:

The volume of Cylinder A is $\pi\times2^2\times8=32\pi$ , and so the
volume of water in Cylinder A is $\frac34\times32\pi=24\pi$ .

If all of the water from Cylinder A is poured into Cylinder B, the
volume of water in Cylinder B is $24\pi$ .

The volume of Cylinder B is $\pi\times8^2\times2=128\pi$ , and so the
fraction of Cylinder B that is full of water is $\dfrac{24\pi}{128\pi}=\dfrac{3}{16}$ .

Solution 2:

As in Solution 1, the volume of water in Cylinder B would be $24\pi$ .

Suppose that the height of the water in Cylinder B is $h$ .

Then, $\pi\times8^2\times h=24\pi$
or $h=\dfrac{24\pi}{64\pi}=\dfrac{3}{8}$ .
Since the height of Cylinder B is $2$
and the height of the water is $\dfrac38$ , then the fraction of Cylinder B
that is full of water is $\dfrac{3/8}{2}=\dfrac{3}{16}$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.