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.

Question

johnweldon1993 · Answer

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
$$\large 20:8$$