To find the surface area of the dilated cube, we can follow these steps:
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Determine the side length of the dilated cube: The original side length of the cube is 8 centimeters. If the cube is dilated by a scale factor of 14, the new side length will be: \[ \text{New side length} = \text{Original side length} \times \text{Scale factor} = 8 , \text{cm} \times 14 = 112 , \text{cm} \]
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Calculate the surface area of the dilated cube: The surface area \(A\) of a cube is given by the formula: \[ A = 6s^2 \] where \(s\) is the length of a side of the cube. Using the new side length: \[ A = 6(112 , \text{cm})^2 \]
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Calculate \(112^2\): \[ 112^2 = 12544 , \text{cm}^2 \]
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Calculate the surface area: \[ A = 6 \times 12544 , \text{cm}^2 \] \[ A = 75264 , \text{cm}^2 \]
Thus, the surface area of the dilated cube is 75264 cm².
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