Question

The volume of this sphere is 1570/3 cubic inches. What is its radius?

Answer 1

1570/3 in terms of pi is
`(500\pi)/(3)`. That's our given volume. It just make it easier to me since there is a pi in the volume formula for a sphere, which is
`V=(4)/(3)\pi r^3`. Replacing the V with our given volume the formula looks like this:
`(500\pi)/(3) =(4)/(3)\pi r^3`. If we start by mulitplying both sides by 3, the 3's in both denominators cancel out leaving us with
`500\pi =4\pi r^3`. We divide both sides by 4pi and the pi's cancel out anyways.
`(500\pi)/(4\pi) =r^3`. Doing that division you get
`r^3=125`. Taking the cubed root of 125 gives us that the radius is 5. So your answer is 5.