Question

a rectangular prism has a length of 12 units, a width of 8 units, and a height of 10. what is the volume of a rectangular pyramid with the same base dimensions and height as the prism? use the keypad to type your answer in the box provided. the volume of the pyramid is cubic units.

Explanation:

Step1: Calculate the base area of the pyramid

The base of the pyramid is a rectangle. The area of a rectangle is \(A = length\times width\). Given \(length = 12\) units and \(width=8\) units, so \(A=12\times8 = 96\) square units.

Step2: Use the volume formula for a rectangular pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. We know \(A = 96\) square units and \(h = 10\) units. Then \(V=\frac{1}{3}\times96\times10\). First, calculate \(96\times10=960\), then \(V=\frac{960}{3}=320\) cubic units.

Answer:

320