Exercise 37 Page 73

Let's first analyze Alex's solution, then Emily's solution.

Alex's Solution

We are given the rectangular prism that is shown below.

Alex calculated the surface area of the given rectangular prism the following way. (5* 3)* 6faces=90in^2 By multiplying 5* 3 Alex calculates the area of the longest face. Then, Alex multiplies it by 6, as if all the faces of the prism were equal. If the given solid was a cube, Alex's calculations would be correct. However, from the diagram we can see that the solid is not a cube and some of the faces have different surface area. Therefore, Alex's solution is not correct.

Emily's Solution

Let's now have a look at Emily's solution. 2(5* 4* 3)=120in^2 By multiplying 5* 4* 3 Emily calculates the volume of the prism. Since the lengths of the edges are measured in inches, the product is measured in inches cubed. 5in* 4in* 3in=60 in^3 That results in a contradiction, as her answer is measured in inches squared. Emily's solution is also incorrect.

Correct Solution

Examining the diagram, we can see that the rectangular prism has 3 pairs of equal faces. We can calculate the surface area of the prism using the following formula. S=2(ab+bc+ac), Here a, b and c are the lengths of the edges. Let's substitute a with 3, b with 4, and c with 5 into the formula and calculate S.

The correct surface area of the rectangular prism is 94in^2.