Question

There are two concentric spheres of radii 3 units and 6 units. What is the volume, in cubic units, of the region within the larger sphere and not within the smaller sphere

Answer 1

Check the picture below.

we can simply get the volume of the larger sphere, then the volume of the smaller sphere and subtract it from that of the larger sphere and what's leftover is the region between both.

$\stackrel{\textit{\large volumes}}{\stackrel{\textit{sphere with r=6}}{\cfrac{4\pi (6)^3}{3}}~~ -~~\stackrel{\textit{sphere with r = 3}}{\cfrac{4\pi (3)^3}{3}}}\implies 288\pi -36\pi \implies 252\pi \approx \stackrel{cubic~units}{791.68}$