Asked by Ian
The solid below is dilated by a scale factor of 3. Find the volume of the solid created upon dilation. Answer in terms of piπ. The number for the line inside of a sphere is 6.
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GPT-5 mini
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I’m missing the diagram, so is the labeled 6 the radius or the diameter of the sphere? Here are both possibilities:
- If 6 is the diameter: original radius r = 6/2 = 3.
Original volume = (4/3)π(3^3) = 36π. Dilation by factor 3 multiplies volume by 3^3 = 27, so new volume = 36π · 27 = 972π.
- If 6 is the radius: original radius r = 6.
Original volume = (4/3)π(6^3) = 288π. After dilation by 3, new volume = 288π · 27 = 7776π.
Tell me which measurement the 6 labels and I’ll confirm the final answer.
- If 6 is the diameter: original radius r = 6/2 = 3.
Original volume = (4/3)π(3^3) = 36π. Dilation by factor 3 multiplies volume by 3^3 = 27, so new volume = 36π · 27 = 972π.
- If 6 is the radius: original radius r = 6.
Original volume = (4/3)π(6^3) = 288π. After dilation by 3, new volume = 288π · 27 = 7776π.
Tell me which measurement the 6 labels and I’ll confirm the final answer.
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