Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.The area

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Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.The area

of the base of the cube, B, is square units.The volume of the cube is blank cubic units.The height of each pyramid, h, is blank . Therefore,b = 2h.There are square pyramids with the same base and height that exactly fill the given cube.Therefore, the volume of one pyramid is blank or One-third.

Mathematics

1 answer:

Viefleur [7K] · Answer 1 · 2022-02-23T08:45:53+03:00

Step-by-step explanation:

Cubes have square faces, so the area of the base is b².

The volume of the cube is b³.

The height of each pyramid is half the height of the cube, so h = b/2. Which means b = 2h.

The cube is made of 6 square pyramids with the same base and height. Therefore, each pyramid has 1/6 the volume of the cube. So the volume of each pyramid is b³/6.