Chapter 6.6, Problem 10PPS

a.

To determine

To find: The length of Roosevelt’s moustache on the monument.

Answer to Problem 10PPS

20 ft.

Explanation of Solution

Given information:

The scale model of the actual Mount Rushmore carving is $1\text{ in}\text{.}=1\text{ ft}\text{.}$ Teddy Roosevelt’s moustache was 1 foot 8 inches long on the model.

Calculation:

Let x be the length of Roosevelt’s moustache on the monument.

Then by proportion,

  $\begin{array}{l}\frac{1\text{ in}\text{.}}{1\text{ ft}\text{.}}=\frac{1\text{ ft 8 in}\text{.}}{x\text{ ft}\text{.}}\\ \Rightarrow \frac{1\text{ in}\text{.}}{1\text{ ft}\text{.}}=\frac{20\text{ in}\text{.}}{x\text{ ft}\text{.}}[1\text{ ft 8 in}\text{.=12+8 in}\text{.=20 in}\text{.]}\\ \Rightarrow 1\times x=20\times 1\text{ [By cross multiplication]}\\ \Rightarrow x=20\end{array}$

Thus, the length of Roosevelt’s moustache on the monument is 20 ft.

b.

To determine

To find: The scale factor.

Answer to Problem 10PPS

  $\frac{1}{12}$

Explanation of Solution

Given information:

The scale model of the actual Mount Rushmore carving is $1\text{ in}\text{.}=1\text{ ft}\text{.}$

Calculation:

The ratio of the length of the model to the length of the monument is $\frac{1\text{ inch}}{1\text{ foot}}$ .

Then, the scale factor is,

  $\begin{array}{l}\frac{1\text{ inch}}{1\text{ foot}}\\ =\frac{1\text{ inch}}{12\text{ inches}}[\because 1\text{ foot=12 inches]}\\ =\frac{1}{12}\end{array}$

c.

To determine

To find: The height of George Washington’s face on the model.

Answer to Problem 10PPS

60 inches

Explanation of Solution

Given information:

The scale model of the actual Mount Rushmore carving is $1\text{ in}\text{.}=1\text{ ft}\text{.}$ The length of George Washington’s face is 60 feet tall on the monument.

Calculation:

Let x be the height of George Washington’s face on the model.

Then by proportion,

  $\begin{array}{l}\frac{1\text{ in}\text{.}}{1\text{ ft}\text{.}}=\frac{x\text{ in}\text{.}}{\text{60 ft}\text{.}}\\ \Rightarrow 1\times 60=x\times 1\text{ [By cross multiplication]}\\ \Rightarrow 60=x\\ \Rightarrow x=60\end{array}$

Thus, George Washington’s face is 60 inches tall on the model.