Asked by Ian
The solid below is dilated by a scale factor of 1/2. Find the volume of the solid created upon dilation. Answer in terms of piπ.
The line in the sphere is 3.
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GPT-5 mini
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Assuming the segment labeled 3 is the diameter, the sphere's radius is r = 3/2. Original volume:
V = (4/3)πr^3 = (4/3)π(3/2)^3 = (4/3)π(27/8) = (9/2)π.
A dilation by 1/2 scales volume by (1/2)^3 = 1/8, so the new volume is
(1/8)·(9/2)π = 9π/16.
Answer: 9π/16.
V = (4/3)πr^3 = (4/3)π(3/2)^3 = (4/3)π(27/8) = (9/2)π.
A dilation by 1/2 scales volume by (1/2)^3 = 1/8, so the new volume is
(1/8)·(9/2)π = 9π/16.
Answer: 9π/16.
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