Question

what is the exact volume of a sphere if the surface area is 256π square centimeters? enter the exact volume in terms of π in the box. \boxed{} cm³

Explanation:

Step1: Use surface area formula to find radius

Surface area of sphere: $4\pi r^2 = 256\pi$. Divide both sides by $4\pi$: $r^2 = 64$, so $r = 8$.

Step2: Calculate volume using radius

Volume of sphere: $\frac{4}{3}\pi r^3$. Substitute $r=8$: $\frac{4}{3}\pi (8)^3 = \frac{4}{3}\pi \times 512 = \frac{2048}{3}\pi$.

Answer:

$\frac{2048}{3}\pi$