A metallic sphere initially has radius R. Its temperature rises by a small amount ΔT; the coefficient of linear expansion is α. Find the approximate increase in the sphere's volume.
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Question

A metallic sphere initially has radius R. Its temperature rises by a small amount ΔT; the coefficient of linear expansion is α. Find the approximate increase in the sphere's volume.

G1 Physics · Accepted Answer

Step 1: Initial volume V = (4/3)πR³. Step 2: For an isotropic solid with small temperature change, the coefficient of volume expansion is approximately β = 3α. Step 3: Increase in volume is ΔV = βVΔT = 3α × (4/3)πR³ × ΔT. Step 4: Simplify: ΔV = 4πR³αΔT. Final answer: 4πR³αΔT (Option C).