Given, diameter of sphere =D Initial surface area, A=4πR2 ‌=4π(‌
D
2
)2 ‌=πD2.....(i) Surface area after heating by temperature δT, A′=4π(‌
D′
2
)2=π(D′)2.....(ii) where D′ is the new diameter. From the equation of lincar expansion, we have D′=D(1+αδT)......(iii) putting the value of D′ from eq. (iii) in cq. (ii) we get A′‌=πD2(1+αδT)2 ‌=πD2(1+α2δT2+2αδT)......(iv) ‌=πD2(1+α2δT2+2αδT)−πD2 ‌=πD2[1+α2δT2+2αδT−1] ‌=πD2[α2δT2+2αδT] ‌ Change in surface area ‌‌=A′−A=πD′2−πD2 ‌=πD2αδT(α.δT+2)