In two square pyramids of the same volume, the base edge of one is half the base edge of the other. How many times the height of the pyramid with larger base is the height of the other?

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Solution

Let the base edge of the second pyramid be b units.

∴ Base edge of the first pyramid = units

Let the height of the first and the second pyramid be h₁ units and h₂ units respectively.

Base area of the first pyramid = ( units)² = sq. units

Base area of the second pyramid = (b units)² = b² sq. units

Volume of square pyramid = Base area × Height

According to given condition:

Volume of the first pyramid = Volume of the second pyramid

Therefore, the height of the pyramid with larger base is one-fourth times the height of the other.

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