ASVAB Mathematics Knowledge Practice: Volume

On the Mathematics Knowledge subtest on the ASVAB, questions involving three-dimensional figures may jump off the screen at any time. You should be ready for them by memorizing the volume formulas for the most common 3D figures, like spheres, cubes, and pyramids.

Practice questions

1. Find the volume of the right square pyramid:

   

   A. 450 cm³ B. 500 cm³ C. 1,500 cm³ D. 150 cm³

2. Find the volume:

   

   A. 960 mm³ B. 480 mm³ C. 120 mm³ D. 840 mm³

Answers and explanations

1. The correct answer is Choice (B).

   The formula for the volume of a pyramid is

   

   where B is the area of the pyramid's base and h is the pyramid's height. You're dealing with a right square pyramid, so the base is a square. Because a square has an area of A = s² (where s is the length of one side of the base), you can write the formula as

   

   Replace the variables with the numbers you know:

   

2. The correct answer is Choice (A).
   The formula for volume of a right rectangular prism is V = lwh, with l representing length, w representing width, and h representing height: