Chapter 6.6, Problem 42E

a.

To determine

To write the scale of the penny to the mask without units

Answer to Problem 42E

The scale of the penny is 1 :28.36

Explanation of Solution

Given information:

Given the height of a mask is $9\frac{3}{4}\text{ inches}$

Calculation:

  $\begin{array}{l}\text{Profile of Lincon's head,}\\ \text{height of a penny =}\frac{11}{32}\text{ inches}\\ \text{height of a mask}=9\frac{3}{4}\text{ inches =}\frac{39}{4}\text{ inches}\\ \text{Therefore,}\\ \text{scale }\frac{39}{4}÷\frac{11}{32}\\ \Rightarrow \frac{39}{4}\times \frac{32}{11}=28.36\\ \Rightarrow \text{scale =1 :28}\text{.36 }\\ \end{array}$

b.

To determine

To write the scale of a mask to the carvings without units

Answer to Problem 42E

The scale of the mask to the carvings is 1: 6.15

Explanation of Solution

Given information:

Given the height of a mask is $9\frac{3}{4}\text{ inches}$

Calculation:

The length of a carving is 60 feet high

  $\begin{array}{l}60÷\frac{39}{4}=6.15\\ \Rightarrow 1:6.15\end{array}$

c.

To determine

To write the scale of the penny to the carvings without units

Answer to Problem 42E

The scale of the penny to the carvings is 1:174.55

Explanation of Solution

Given information:

Given the height of a mask is $9\frac{3}{4}\text{ inches}$

Calculation:

  $\begin{array}{l}\text{Profile of Lincon's head,}\\ \text{height of a penny =}\frac{11}{32}\text{ inches}\\ \Rightarrow \text{60}÷\frac{11}{32}=174.55\\ \Rightarrow 1:174.55\end{array}$

d.

To determine

To find the length of lincoln’s nose on the carvings and on the mask

Answer to Problem 42E

The length of lincoln’s nose is 131 inches

Explanation of Solution

Given information:

Given the length of Lincoln’s nose

Calculation:

  $\begin{array}{l}\text{Nose on penny is }\frac{1}{16}\text{ inch}\\ \text{nose of carving}\\ \Rightarrow \frac{1}{174.55}=\frac{\frac{1}{16}}{x}\\ \Rightarrow x=\frac{1}{16}\times 174.55\\ \Rightarrow x=10.91\text{ feet}\\ \Rightarrow x=130.9\text{ inches}\\ \Rightarrow x=131\text{ inches}\end{array}$