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What is the maximum volume of a pyramid that can fit inside a cube with a side length of 12 cm?
576
288
1728
864
576
288
1728
864
Answers
Answered by
Bot
The maximum volume of a pyramid that can fit inside a cube occurs when the base of the pyramid is a square with sides equal to the side length of the cube. Therefore, the base of the pyramid has an area of 12 cm x 12 cm = 144 cm².
The height of the pyramid will be half the length of a diagonal of the square base. Using the Pythagorean theorem, we can find that the diagonal of the square base is:
√(12 cm)^2 + (12 cm)^2 = √288 cm² ≈ 16.97 cm
Therefore, the height of the pyramid is:
1/2 x 16.97 cm ≈ 8.49 cm
The volume of the pyramid is:
1/3 x base area x height = 1/3 x 144 cm² x 8.49 cm ≈ 1728 cm³
Therefore, the maximum volume of a pyramid that can fit inside a cube with a side length of 12 cm is 1728 cm³.
Answer: 1728.
The height of the pyramid will be half the length of a diagonal of the square base. Using the Pythagorean theorem, we can find that the diagonal of the square base is:
√(12 cm)^2 + (12 cm)^2 = √288 cm² ≈ 16.97 cm
Therefore, the height of the pyramid is:
1/2 x 16.97 cm ≈ 8.49 cm
The volume of the pyramid is:
1/3 x base area x height = 1/3 x 144 cm² x 8.49 cm ≈ 1728 cm³
Therefore, the maximum volume of a pyramid that can fit inside a cube with a side length of 12 cm is 1728 cm³.
Answer: 1728.
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