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EEJ MAIN Aptitude QUESTION #10995
Question 1
A square pyramid has a base of side $2a$ and all lateral edges of length $a\sqrt{5}$. A plane parallel to the base cuts the pyramid at half its height. What is the ratio of the volume of the frustum to the volume of the original pyramid?
  • $\frac{7}{8}$✔️
  • $\frac{3}{4}$
  • $\frac{5}{8}$
  • $\frac{1}{2}$
Correct Answer Explanation
At half the height, the linear dimensions of the top smaller pyramid are half. So its volume is $(\frac{1}{2})^3 = \frac{1}{8}$ of the original. The frustum volume is $1 - \frac{1}{8} = \frac{7}{8}$ of the original pyramid.