Pyramid

Geometry Level pending

The volume of the rectangular parallelepiped shown above is 1600 cubic units. A pyramid is to be formed by connecting the points A and M, B and M, M and C, and H and M. Find the volume of the pyramid in cubic units. Round off your answer to the nearest hundreds.


The answer is 500.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The volume of pyramid is given by V = 1 3 A h V = \frac 13 Ah , where A A is the base area and h h is the height. Therefore, the volume of the pyramid is 1 3 \frac 13 that of the volume of the rectangular parallelepiped whatever the height that is V = 1600 3 ≈ 500 V = \frac {1600}3 \approx \boxed{500} .

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@Marvin Kalngan The condition of "if the height of the rectangular parallelepiped is a positive integer and a perfect cube less than 10. " doesn't make sense to me. We know that the volume of the payramid is always 1/3 the volume of the parallelpiped.

Calvin Lin Staff - 4 years, 7 months ago

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