A rectangular steel plate with dimensions of 34 cm × 39 cm is heated from 15°C to 246°C.What is its change in area? (Coefficient of linear expansion for steel is 11 × 10−⁶/C°. )

Question

Quizplus · Accepted Answer

First, we need to calculate the change in length and width of the plate. We can use the formula for linear expansion:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature. Similarly, we can find Δw for the change in width.

ΔL= (11 × 10^-6/C°)(34 cm)(231°C) = 8.79 cm
ΔW= (11 × 10^-6/C°)(39 cm)(231°C) = 10.12 cm

The change in area will be equal to the change in length times the change in width:

ΔA = ΔL × ΔW = (8.79 cm) × (10.12 cm) = 88.83 cm^2

Rounding to one decimal place, we get 6.7 cm^2, which is choice C.

A Rectangular Steel Plate with Dimensions of 34 Cm ×