Using the quadratic formula, the solutions are x1 = 1.3416 and x2 = -1.3416
So, it has 2 real solutions.
From the facts given, the swimming pool and the floor of the gym has the same in size. The pool has a dimension of 75 ft by 60 ft. Basically, the possible size of the gym floor is also 75 ft by 60 ft.
You did everything right. The correct answer is 191
Hope this helps
The two parabolas intersect for

and so the base of each solid is the set

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas,
. But since -2 ≤ x ≤ 2, this reduces to
.
a. Square cross sections will contribute a volume of

where ∆x is the thickness of the section. Then the volume would be

where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

We end up with the same integral as before except for the leading constant:

Using the result of part (a), the volume is

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

and using the result of part (a) again, the volume is
