PSAT Math Grid-Ins Question 71: Answer and Explanation

Question: 71

For a school project, a student wants to build a replica of the Great Pyramid of Giza out of modeling clay. The real Great Pyramid has a square base with side length 750 feet and a height of 500 feet. If the student has 162 cubic inches of clay for her model, what height will her pyramid be in inches?

(The formula for the volume of a pyramid is and is provided in your test booklet.)

Correct Answer: 6

Explanation:

6

Difficulty: Hard

Getting to the Answer: The formula for the volume of a pyramid is . The pyramid has a square base, so the length and width are equal. The proportion of the length:width:height is 750:750:500, which reduces to 3:3:2. Expressed with a common multiplier, this is 3x:3x:2x.

Putting these proportions into the volume equation gives you:

The question states that the student has 162 cubic inches of modeling clay, so this value can be input for V to solve for x as follows:

The last piece to remember is that height in the equation was replaced with 2x, so the height of the student's model will be 6 inches. Grid in 6.