Question

Sphere of radius 7 inches is placed inside a rectangular prism with length 15 inches width 18 inches in height 20 inches what is the volume of the prism not occupied by the sphere

Answer 1

Check the picture below.

so let's simply get the volume of the sphere, then the volume of the prism, and then subtract the one from the sphere from that of the prism, and what's leftover, is the volume not occupied by the sphere, voila!!

`\stackrel{\textit{\LARGE volumes}}{\stackrel{rectangular~prism}{(20)(15)(18)}~~ - ~~\stackrel{sphere}{\cfrac{4\pi (7)^3}{3}}}\implies 5400-\cfrac{1372\pi }{3} ~~ {\LARGE \begin{array}{llll} \approx ~~ 3963.24~in^3 \end{array}}`