ISEE Word Problems Question 213: Answer and Explanation
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Question: 213
1. The formula for the volume of a pyramid with a square base is 
Bh, where B represents the area of the square base of the pyramid and h represents the height of the pyramid. The volume of Pyramid A is one half the volume of Pyramid B. Which of the following statements could be true?
- A. The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the two times a side of the base of Pyramid B.
- B. The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the same as a side of the base of Pyramid B.
- C. A side of the base of Pyramid A is one half a side of the base of Pyramid B, and the height of Pyramid A is the same as the height of Pyramid B.
- D. Both a side and the height of Pyramid A are one half a side and the height of Pyramid B.
Correct Answer: B
Explanation:
The answer is B
If Pyramid B has a base with side length s and a height of h, the volume VB = s2h. Pyramid A, therefore, has a volume VA = 
s2h. Test each answer using the given volume formula. For choice (A), the height is 
h, and the side length is 2s, making the volume VA = 
. Eliminate choice (A). For choice (B), the height is 
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