Question

Find the diameter of a sphere with the volume 7776pi in^3

Answer 1

Answer:

The diameter is 36 inches

Step-by-step explanation:

The volume of a sphere is

$\frac{4}{3} \pi {r}^{3}$

The given sphere has volume

$7776\pi {in}^{3}$

We can now equate the formula to the given volume and solve for r.

$\frac{4}{3} \pi {r}^{3} = 7776\pi$

${r}^{3}= 7776\pi \times \frac{3}{4\pi}$

${r}^{3} = 5832$

$r = \sqrt[3]{5832}$

$r = 18$

The diameter of the sphere is twice the radius.

Hence

$diameter = 2 \times 18 = 36in$