Question

Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid? A. The height of each pyramid is 1/2 h units. B. The height of each pyramid is 1/3 h units. C. The height of each pyramid is 1/6 h units. D. The height of each pyramid is h units.

Answer 1

The correct answer is (C.) The height of each pyramid is 1/6 h units, because six identical pyramids would stack up to the same height as the cube they fill.

Step-by-step explanation:

In the context of geometry, the volume of a pyramid is given by the formula 1/3 x base area x height. If six identical pyramids fill the same volume as a cube with the same base, it means their combined heights would be equal to that of the cube.

So, if the height (h) of the cube is considered, the height of each pyramid would be 1/6 of the height of the cube as the six pyramids would stack up to the same height.

Therefore, the correct answer is (C.) The height of each pyramid is 1/6 h units.

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