WAEC Physics 2012 Paper

Concept: When a solid sheet is heated, its area increases according to the area expansivity, which is twice the linear expansivity.Explanation: Given: initial area $A_1 = 100\,\mathrm{cm}^2$, temperature rise $\theta = 70\,{}^\circ\mathrm{C}$, linear expansivity $\alpha = 0.000017\,\mathrm{K}^{-1}$.The area expansivity is $\beta = 2\alpha$.So, $\beta = 2 \times 0.000017 = 0.000034\,\mathrm{K}^{-1}$.The formula for the new area is $A_2 = A_1(1 + \beta\theta)$.Substitute the values: $A_2 = 100(1 + 0.000034 \times 70)$.Calculate the product: $0.000034 \times 70 = 0.00238$.Thus, $A_2 = 100(1 + 0.00238) = 100(1.00238)$.This gives $A_2 = 100.238\,\mathrm{cm}^2$.Rounded to two decimal places, the new area is $100.24\,\mathrm{cm}^2$.Answer: The new area is $100.24\,\mathrm{cm}^2$, which is option C.