Question

The volume of the sphere is 500/3pi cubic units. What is the value of x

Answer 1

Explanation:

Formula for the volume of a sphere is V = (4/3) (π) r³

3V 4²

and so the cube of the radius, "r," is r³ = ------------- * -----

4 4²

Taking the cube root of both sides, we get

∛[3V / 4²] 3V

and so the radius, "r," is r = ------------------ = ∛ ( --------- ) = (1/4)*∛(3*v)

∛[4³] 4³

Then

r = (1/4)*∛(3*V), after substituting 500/(3π) for V, becomes:

r = (1/4)*∛[ 3*500/3π ] = (1/4)*∛[ 500/π ]