Question

Find the ratio of the volumes of a larger sphere with a diameter of 20 inches and a smaller sphere with a diameter of 8 inches. Reduce to lowest terms and write your answer in the form a:b. Do not include units.

Answer 1

Well the volume of a sphere is

\[\large \frac{4}{3}\pi r^3\]

So the bigger sphere will be

\[\large \frac{4}{3}\pi (20)^3\]
And the smaller will be
\[\large \frac{4}{3}\pi (8)^3\]

So for the ratio...set them equal to each other

\[\large \frac{4}{3}\pi (20)^3 = \frac{4}{3}\pi (8)^3\]

Now notice...both side have \(\large \frac{4}{3}\) and \(\large \pi \) and something raised to the thrid power....well all that cacels each other out...so all we have left after all that is merely
\[\large 20:8\]