Question

two spheres cut for uniform rock. one has radius of 4.5 cm the other has a mass 5 times greater what is the radius of the other sphere?
answer is 7.69cm
How is this setup?

Answer 1

The formula for the volume of a sphere is
\[volume=\frac{4}{3}\pi r ^{3}\]
The two spheres are cut from uniform rock, therefore their masses are proportional to their volumes. So we can write:
\[\frac{\frac{4}{3}\pi (4.5)^{3}}{\frac{4}{3}\pi r ^{3}}=\frac{4.5^{3}}{r ^{3}}=\frac{1}{5}\]
\[r ^{3}=5\times 4.5^{3}\]
\[r=\sqrt[3]{5\times 4.5^{3}}\]