Chapter 1.5, Problem 40E

a.

To determine

To write: formula for the surface area of the given rectangular prism.

Answer to Problem 40E

  $S=2b^2+4bl$

Explanation of Solution

The surface area of an object is the sum of areas of all its faces.

This prism has 4 rectangular faces of length l and width b, and 2 square faces of side length b.

Now, $\text{Area of rectangle = length}\times \text{width}$ and ${\text{Area of square = side}}^2$

Thus, the surface area of the prism is,

  $S=2b^2+4bl$

b.

To determine

To rewrite: the formula obtained in part (a) for one of the side lengths b or l and explain the reason for choosing that side length.

Answer to Problem 40E

  $l=\frac{S-2b^2}{4b}$

Explanation of Solution

Consider,

  $\begin{array}{r}S=2b^2+4bl\\ S-2b^2=4bl\\ l=\frac{S-2b^2}{4b}\end{array}$

The reason for choosing side length l is that the formula $S=2b^2+4bl$ is linear for l but for the side length b this formula is quadratic which makes it more complicated.