GED Math Extra Prep: Volume and Surface Area of Prisms
The GED Math test will throw some geometry questions at you that involve three-dimensional shapes like prisms. Usually, they will be in the form of a cube or box, as in the following practice questions.
- A cube has a surface area of 216 square inches. What is its volume in cubic inches?
- If these two boxes have the same volume, what is the height of the second box?
Answers and Explanations
- The correct answer is D.
You can determine the surface area (SA) of a cube with the following equation, in which s is the length of a side:
SA = 6s2
You know the surface area equals 216 cubic inches, so you can substitute this into the equation for SA and solve for s:
216 = 6s2
Dividing both sides by 6 gives you
36 = s2
Hence, s = 6.
A cube is a special type of rectangular prism in which the length (l), the width (w), and the height (h) are all equal. The volume of a rectangular prism is given by
V = lwh
Substituting l = 6, w = 6, and h = 6 into the equation shows the volume equals 216 cubic inches. Hence, Choice (D) is the correct answer.
- The correct answer is B.
The volume of a box (rectangular prism) is V = lwh, where l is the length, w is the width, and h is the height. Set the volumes of the two boxes equal to each other and solve for h:
Therefore, Choice (B) is the correct answer.