You have designed a model of a square-based pyramid in honor of your calculus teacher. The height will be $10$ inches. The equation of one side of the pyramid is: $f(x) = -0.5x + 10$.

1. Sketch a diagram of your pyramid. A complete diagram includes the function, the $x$- and $y$-axes, and a typical slice labeled with the appropriate dimensions.

   Hint (a):

   Pyramids have pointy tips. If the height is $10$ inches, the base would start at $y = 0$.

2. Set up and evaluate an integral that calculates the exact volume of your pyramid.

   Hint (b):

   Notice that the cross-sections are perpendicular to the $y$-axis, so set up and evaluate an integral in terms of $y$.

   $V=\int_{y=a}^{y=b}\text{area }dy$