Exercise 33 Page 868

The volume of a cylinder with the radius r and height h can be calculated by the following formula. V=π r^2 h We are given the height h = 6in. We know the surface area S=144πin^2, so we can find the radius using the following formula. S=2π rh+2π r^2 In this formula, r is the radius of the base and h is the height of the cylinder. Substituting S with 144π and h with 6 into the formula, we can solve for r. Let's do it!

We have found that r is either 6 or -12. Since a negative length radius does not make sense, we know that r = 6. We can now substitute 6 for r and 6 for h into the appropriate formula to calculate the volume of the cylinder.

The approximate volume of the given cylinder is 678.6 in^3.