A square hole,30 cm on each edge,is cut in the center of a square aluminum plate 1 m on a side.The coefficient of linear expansion of aluminum is 2.4 $\times$ 10^-5/Cº.If the plate is heated 25 ºC above the starting temperature,the area of the hole A)increases by 1.1 cm². B)increases by 0.54 cm². C)increases by 0.00060 cm². D)decreases by 0.54 cm². E)decreases by 0.00060 cm².

Question

Quizplus · Accepted Answer

The initial area of the hole is (30 cm)^2 = 900 cm^2.
The initial area of the plate is (100 cm)^2 = 10,000 cm^2.
When heated 25 ºC, the plate expands by:
10,000 cm^2 * 2.4 x 10^-5/ºC * 25 ºC = 6 cm^2
The area of the hole also expands by the same coefficient of linear expansion, so the new area of the hole is:
900 cm^2 * 2.4 x 10^-5/ºC * 25 ºC = 0.54 cm^2
Therefore, the area of the hole increases by:
0.54 cm^2 - 0.90 cm^2 = 0.64 cm^2
This is approximately 1.1 cm^2 rounded to one decimal place, so the best choice is A.

A Square Hole,30 Cm on Each Edge,is Cut in the Center