Question

slicing

Answer 1

I have no idea what "slicing" is, but I guess it has something to do with integration. So! To integrate this we need an axis, lower and upper bounds, and an area to integrate along dx. The lower and upper bounds are determined by the height of said object. Which is √(4.5^2+9^2).

How do we graph the change in area versus change in height? Well, area is r^2, and if our said object was perpendicular to the x-axis, its area could be determined a la the sides squared. A max half-side of 4.5 over a distance of √(4.5^2+9^2); knowing the slope is constant, we write this as 4.5x/√(4.5^2+9^2); however, this being area, we need to full side length, so 9x/√(4.5^2+9^2), and we need to square this, so (9x/√(4.5^2+9^2))^2.

Now, let's integrate this with respect to x, yes?

∫_{0,√(4.5^2+9^2)}((9x/√(4.5^2+9^2))^2)dx