### Home > APCALC > Chapter 8 > Lesson 8.3.3 > Problem8-124

8-124.

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.

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.

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

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

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 8-124 HW eTool