Question 577418
The only problem is, we do not know what function f(x) defines the outer (curved) edge of the building, so we cannot find an exact value. Additionally, this function is not one-to-one so we would have to partition this function to have an inverse function.


Suppose f(x) is defined only on [0,75]. The cross-sectional area of the building bounded by x=0, x=75, y=112.5 is equal to


*[tex \LARGE A = \int_{0}^{75} f(x)dx]


We can write this integral in terms of dy, but we don't have to since it's a definite integral and we will still get the same result.


The cross-sectional area of each floor is given by *[tex \LARGE 2.5(75 - f^{-1}(2.5x))]. We find this by subtracting off area from a rectangle of size 2.5 * 75. Sum this from x = 1 to x = f, where f is the last floor counted:


*[tex \LARGE A_1 = \sum_{i = 1}^{f} 2.5(75 - f^{-1}(2.5x))]


The error E is taken by finding A - A1:


*[tex \LARGE E = A - A_1 = \int_{0}^{75} f(x)dx - \sum_{i = 1}^{f} 2.5(75 - f^{-1}(2.5x))]


However you want to multiply this by 2, because we only accounted for half of the building. Therefore the area of what you want is 2E. To find the volume, multiply by the width of the building (72 m).