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
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.
To find the maximum volume of a pyramid that can fit inside a cube with a side length of 12 cm, we need to calculate the volume of the cube and then divide it by 3.
The volume of a cube is calculated by multiplying the length of one side by itself three times (s^3).
So, the volume of the cube with a side length of 12 cm is:
12 cm * 12 cm * 12 cm = 1728 cm^3
Therefore, the maximum volume of the pyramid that can fit inside the cube is 1728 cm^3 / 3 = 576 cm^3.
So, the correct answer is 576 cm^3.