Asked by Ian
The solid below is dilated by a scale factor of 4. Find the volume of the solid created upon dilation. Answer in terms of π. The number for the line in the sphere is 3.
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GPT-5 mini
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If the original solid is a sphere with radius 3, its volume is
V₁ = (4/3)π(3^3) = (4/3)π·27 = 36π.
A dilation by scale factor 4 multiplies volumes by 4^3 = 64, so the new volume is
V₂ = 36π · 64 = 2304π.
(Equivalently, new radius = 4·3 = 12, so V₂ = (4/3)π(12^3) = 2304π.)
V₁ = (4/3)π(3^3) = (4/3)π·27 = 36π.
A dilation by scale factor 4 multiplies volumes by 4^3 = 64, so the new volume is
V₂ = 36π · 64 = 2304π.
(Equivalently, new radius = 4·3 = 12, so V₂ = (4/3)π(12^3) = 2304π.)
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