To find the volume of the pyramid, we can start by using the information given about the cube.
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Volume of the cube: The volume \(V\) of a cube with side length \(s\) is given by the formula: \[ V = s^3 \] According to the problem, the volume of the cube is 27 cubic inches: \[ s^3 = 27 \] Thus, we find the side length \(s\): \[ s = \sqrt[3]{27} = 3 \text{ inches} \]
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Height of the cube: Since the cube is also defined by its side length, the height of the cube is: \[ \text{Height of the cube} = s = 3 \text{ inches} \]
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Base area of the cube: The base area \(A\) of the cube, which is a square, is given by: \[ A = s^2 = 3^2 = 9 \text{ square inches} \]
Since Mei Li's square-based pyramid has the same height and base area as the cube, the pyramid also has a height of 3 inches and a base area of 9 square inches.
- Volume of the pyramid: The volume \(V\) of a square-based pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] Substituting the values for the base area and height: \[ V = \frac{1}{3} \times 9 \times 3 \] Simplifying it: \[ V = \frac{1}{3} \times 27 = 9 \text{ cubic inches} \]
So, the volume of the pyramid is 9 cubic inches.