Imagine you've got two of these cylinders, both with 1077 cubic cm of water in them, side-by-side.
Now put the rock in one of them, and the water rises 3 cm.If you now hide the lower part of the cylinders, so that you can't see the rock, you'll notice that the cylinder with the rock appears to have more water in it. The "extra" water is currently in the shape of a cylinder (!) with radius 3 cm and radius 7 cm.
The volume of the "extra" water is "area of cross section x height", or
pi x 7 x 7 x 3 cubic cm.
If you are using 22/7 as an approximation to pi, this gives the very tidy answer 462 cubic cm.
If you are using some decimal approximation, like 3.14159, say, the answer is 461.8137.. cubic cm.
This "extra" water is, of course, due entirely to the presence of the rock. Therefore, the volume of the rock must be 462 cubic cm, correct to the nearest cc.
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