To find out how much larger a cube with a side length of 17 feet is compared to a cube with a side length of 12 feet, we first need to calculate the volume of both cubes using the formula for the volume of a cube, which is given by:
\[ V = s^3 \]
where \(V\) is the volume and \(s\) is the side length of the cube.
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Volume of the first cube (side length 17 feet): \[ V_1 = 17^3 = 17 \times 17 \times 17 = 4913 \text{ ft}^3 \]
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Volume of the second cube (side length 12 feet): \[ V_2 = 12^3 = 12 \times 12 \times 12 = 1728 \text{ ft}^3 \]
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Find the difference in volume between the two cubes: \[ V_{\text{difference}} = V_1 - V_2 = 4913 \text{ ft}^3 - 1728 \text{ ft}^3 = 3185 \text{ ft}^3 \]
Thus, the first cube is 3185 ft³ bigger than the second cube.