We have been given that a collar of Styrofoam is made to insulate a pipe. We are asked to find the volume of the given pipe.
We will use volume of hollow cylinder formula to solve our given problem.
[tex]\text{Volume of hollow cylinder}=\pi R^2h-\pi r^2h[/tex], where,
R = Radius of external cylinder,
r = Radius of internal cylinder.
h = Height of cylinder.
Upon substituting our given values in above formula, we will get:
[tex]\text{Volume of hollow cylinder}=\pi (5\text{ in})^2(\text{23 in})-\pi (4\text{ in})^2(\text{23 in})[/tex]
[tex]\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 ((5\text{ in})^2-(4\text{ in})^2)[/tex]
[tex]\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 (25\text{ in}^2-16\text{ in}^2)[/tex]
[tex]\text{Volume of hollow cylinder}=\text{23 in}\cdot 3.14 (9\text{ in}^2)[/tex]
[tex]\text{Volume of hollow cylinder}=649.98\text{ in}^3[/tex]
Therefore, the volume of the pipe is 649.98 cubic inches.
