Question
There is a cube with a side length of 15cm. What is the maximum volume of a square pyramid that can fit inside the cube? Round your answer to the nearest whole number(1 point)
Answers
GPT 3.5
The maximum volume of a square pyramid that can fit inside the cube will be when the base of the pyramid is a square with a side length equal to the diagonal of a face of the cube.
The diagonal of a square is calculated using the formula: diagonal = side length * √2
The diagonal of a face of the cube = 15 * √2
The height of the pyramid is the same as the side length of the cube, which is 15cm.
Therefore, the volume of the square pyramid is calculated using the formula: V = 1/3 * base area * height
The base area = (15 * √2)^2 = 450
The volume = 1/3 * 450 * 15 = 2250
Hence, the maximum volume of a square pyramid that can fit inside the cube is approximately 2250 cubic cm.
The diagonal of a square is calculated using the formula: diagonal = side length * √2
The diagonal of a face of the cube = 15 * √2
The height of the pyramid is the same as the side length of the cube, which is 15cm.
Therefore, the volume of the square pyramid is calculated using the formula: V = 1/3 * base area * height
The base area = (15 * √2)^2 = 450
The volume = 1/3 * 450 * 15 = 2250
Hence, the maximum volume of a square pyramid that can fit inside the cube is approximately 2250 cubic cm.