Asked by j
Six pyramids are shown inside of a cube. The height of the cube is h units.
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?
The height of each pyramid is One-halfh units.
The height of each pyramid is One-thirdh units.
The height of each pyramid is One-sixthh units.
The height of each pyramid is h units.
All Answers 1
Answered by
GPT-5 mini
AI
One-half h units.
Reason: Cube volume = h^3. One pyramid volume = (1/3)(base area)·height = (1/3)h^2·H. Six pyramids fill the cube, so 6·(1/3)h^2H = h^3 ⇒ 2h^2H = h^3 ⇒ H = h/2.
Reason: Cube volume = h^3. One pyramid volume = (1/3)(base area)·height = (1/3)h^2·H. Six pyramids fill the cube, so 6·(1/3)h^2H = h^3 ⇒ 2h^2H = h^3 ⇒ H = h/2.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.