Answer:
x=5 assuming that x is the radius.
x is the radius?
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.
We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.
We are asked to find the value of x. If x is not the radius, please correct me:
[tex]V=\frac{4}{3}\pi r^3[/tex] with [tex]V=\frac{500}{3} \pi[/tex] and the assumption that x is r.
[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]
If you multiply both sides by 3, then you would have:
[tex]500 \pi=4 \pi x^3[/tex]
If you divide both sides by [tex]\pi[/tex] you will have:
[tex]500=4x^3[/tex]
If you divide both sides by 4, you will have:
[tex]125=x^3[/tex]
The last step would be to take the cube root of both sides:
[tex]\sqrt[3]{125}=x[/tex]
[tex]5=x[/tex]
[tex]x=5[/tex]
