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jmc

geometry intermediate

Problem

A particular right square-based pyramid has a volume of 63,960 cubic meters and a height of 30 meters. What is the number of meters in the length of the lateral height () of the pyramid? Express your answer to the nearest whole number.

problem
Solution
The volume is the pyramid is , where is the side length of the base and is the height of the pyramid. Therefore, the area of the base is square meters. Calling the center of the base , we apply the Pythagorean theorem to triangle to get which is closer to meters than to meters, since .
Final answer
50