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What is the value of coefficient of area expansion for a sphere? Assume coefficient of linear expansion is α.

What is the value of coefficient of area expansion for a sphere? Assume coefficient of linear expansion is α. Correct Answer 2α

The area(A) of a sphere is 4πr2. When the temperature increases by ΔT, let change in area be dA. Let the radius increase by dr. The coefficient of area expansion is (dA/A)/ΔT. ∴ dA = 4π(r – dr)2– 4πr2 ≅ 8πrdr. Also, dr = rαΔT. The coefficient of area expansion is (dA/A)/ΔT = (8πr*rαΔT/4π) / ΔT = 2α.

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