Question

What is the volume of a square pyramid that is built in a cube with edges of 12 in

Answer 1

[AI-generated answer — Bot]

The volume of a square pyramid is (1/3) * base area * height. The base area of a cube with edges of 12 in is 12^2 = 144 in^2. The height of the pyramid is also 12 in. Therefore, the volume of the square pyramid is (1/3) * 144 in^2 * 12 in = 576 in^3.

Answer 2

[AI-generated answer — Explain Bot]

To find the volume of a square pyramid, you need to know the base area and the height.

Let's start by finding the height of the square pyramid. Since the square pyramid is built inside a cube, the height will be the same as the edge length of the cube, which is 12 inches.

Now, let's find the base area of the square pyramid. Since the square pyramid is built inside a cube, the base of the pyramid will be a square with side length equal to the edge length of the cube, which is also 12 inches. The formula for the area of a square is side length squared, so the base area will be 12 inches multiplied by 12 inches, which equals 144 square inches.

Now that we have the base area (144 square inches) and the height (12 inches), we can calculate the volume of the square pyramid.

The formula to find the volume of a pyramid is given by: Volume = (1/3) * Base Area * Height

Plugging in the values, we get:
Volume = (1/3) * 144 square inches * 12 inches
Volume = 1/3 * 1728 cubic inches
Volume = 576 cubic inches

Therefore, the volume of the square pyramid built inside a cube with edges of 12 inches is 576 cubic inches.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the volume of a square pyramid built inside a cube, we need to follow these steps:

1. Determine the volume of the cube: Since all edges of the cube are 12 inches, the volume can be calculated using the formula V = s^3, where s is the length of each side. So, V = 12^3 = 1,728 cubic inches.

2. Calculate the volume of the pyramid: The volume of a square pyramid can be calculated using the formula V = (1/3) * B * h, where B is the area of the base and h is the height.

3. Determine the base area of the pyramid: Since the base of the pyramid is square, the area is calculated by multiplying the length of one side by itself. In this case, each side is equal to 12 inches, so the base area is 12 * 12 = 144 square inches.

4. Find the height of the pyramid: Since the pyramid is built inside the cube, the height is equal to the length of the side of the cube.

5. Plug the values into the formula: V = (1/3) * 144 * 12.

6. Simplify the equation: V = (1/3) * 1,728.

7. Calculate the final volume: V = 576 cubic inches.

Therefore, the volume of the square pyramid built inside the cube is 576 cubic inches.