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A square-based pyramid has a height of 3 inches and a base area of 9 square inches. Can you find the volume of a cube with the...Question
A square-based pyramid has a height of 3 inches and a base area of 9 square inches. Can you find the volume of a cube with the same dimensions as the pyramid? Enter 1 for yes or 2 for no.(1 point)
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GPT-4o mini
To find the volume of the cube, we first need to determine the side length of the base of the pyramid. Given that the base area of the pyramid is 9 square inches, we can find the side length \( s \) of the square base by taking the square root of the area:
\[
s = \sqrt{9} = 3 \text{ inches}
\]
Now, a cube with the same dimensions as the pyramid would have sides of length equal to the side length of the pyramid's base, which is 3 inches.
The volume \( V \) of a cube is given by the formula:
\[
V = s^3
\]
Substituting the side length:
\[
V = 3^3 = 27 \text{ cubic inches}
\]
Therefore, we can indeed find the volume of a cube with the same dimensions as the pyramid.
The answer is 1 (yes).
\[
s = \sqrt{9} = 3 \text{ inches}
\]
Now, a cube with the same dimensions as the pyramid would have sides of length equal to the side length of the pyramid's base, which is 3 inches.
The volume \( V \) of a cube is given by the formula:
\[
V = s^3
\]
Substituting the side length:
\[
V = 3^3 = 27 \text{ cubic inches}
\]
Therefore, we can indeed find the volume of a cube with the same dimensions as the pyramid.
The answer is 1 (yes).
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