The length of each edge of an aluminum cube is 0.066 m?

Question

The cube is heated to 135°C from 25°C. What is the increase in the surface area of the cube? (Hint: The length of each edge of the cube expands when heated.)

Answer 1

First, calculate the increase in length of an edge

Expansion coefficient for Al = 23.1 µm/m·K ... ref: http://en.wikipedia.org/wiki/Aluminum

Change in temp = 135-25=110°K

Expansion = 110°K * 0.066 m * 23.1 µm/m·K
= 167 µm = 1.67 x 10^-4 m

New length = .066m + .000167m = .066167m

New Area = 6 sides* (.066167m)^2
= .02627m^2

Old Area = 6 sides* (.066m)^2
=0.02614 m^2

Difference
=.00013 m^2