Question

A sphere has a volume of 457.3 in^3. What is the radius of the sphere?

Answer 1

`\large\boxed{R\approx4.78\ in}`

Explanation:

The formula of a volume of a sphere:

`V=(4)/(3)\pi R^3`

R - radius

We have the volume V = 457.3 in³. Substitute:

`(4)/(3)\pi R^3=457.3\qquad\text{multiply both sides by 3}\\\\4\pi R^3=1371.9\qquad\text{divide both sides by 4}\\\\\pi R^3=342.975\qquad\text{divide both sides by}\ \pi\\\\R^3=(342.975)/(\pi)\qquad/\pi\approx3.14/\\\\R^3\approx(342.975)/(3.14)\\\\R^3\approx109.2277\to R\approx√(109.2277)\\\\R\approx4.78\ in`