A rectangular steel plate with dimensions of 40.0 cm × 30.0 cm is heated from 14.0°C to 164.0°C.What is its change in area? (Coefficient of linear expansion for steel is 11 × 10−⁶/C°. ) A)8.96 cm² B)29.7 cm² C)3.96 cm² D)1.32 cm² E)9.90 cm²

Question

Quizplus · Accepted Answer

First, we need to find the change in length and the change in width individually using the formula:
ΔL = αLΔT and ΔW = αWΔT,
where α is the coefficient of linear expansion, L and W are the original length and width, and ΔT is the change in temperature.

ΔL = (11×10^-6 /°C)(40.0 cm)(150.0°C) = 66.0×10^-4 cm
ΔW = (11×10^-6 /°C)(30.0 cm)(150.0°C) = 49.5×10^-4 cm

The change in area can be found using the formula:
ΔA = (L+ΔL)(W+ΔW) - LW

ΔA = (40.0 cm + 66.0×10^-4 cm)(30.0 cm + 49.5×10^-4 cm) - (40.0 cm)(30.0 cm)
ΔA ≈ 3.96 cm^2

Therefore, the best choice is C, 3.96 cm^2.

A Rectangular Steel Plate with Dimensions of 40