Question

What is the diameter of the sphere?

Answer 1

Remember the equation for the volume of a sphere:

$V = \dfrac{4}{3} \pi r^3$

Since we know the volume, we can set the formula equal to this value and find our radius, and thus our diameter.

$\dfrac{4}{3} \pi r^3 = \dfrac{32}{3} \pi$

• Set up

$r^3 = \dfrac{32}{3} \cdot \dfrac{3}{4}$

• Divide both sides of eqution by $\frac{4}{3} \pi$

$r^3 = 8$

• Multiply right side terms together

$r = 2$

• Take the cube root of both sides

$d = 2(r) = 2(2) = 4$

• Given that $d = 2r$, we find $d = 4$

Our answer is 4 in.