Chapter 6.7, Problem 26SR

a)

To determine

To find: The scale if actual height of the statue of Zeus is given as 40 feet when its height on scale model is given as 8 inches. Also to find the required scale factor between two heights.

Answer to Problem 26SR

Scale on scale model is 1 inch $=5$ feet.

Explanation of Solution

Given information: 

The height of the statue of Zeus on scale model is 8 inches and its actual height is 40 feet.

Concept used:

Scale is actually a comparison between two quantities, that results the one unit of one quantity equals to how much unit of second quantity. Also, scale factor is the ratio between two corresponding given quantities. It is also used the following conversion formula:

1 feet $=12$ inches

Calculation: On comparing two given quantities ,

  $8\text{ inches}=40\text{}\text{feet}$

So, $\begin{array}{c}1\text{ inch}=\frac{40}{8}\text{feet}\\ =5\text{feet}\end{array}$

Based on above calculation, the applied scale is 1 inch= 5 feet.

b)

To determine

To find: The scale if actual height of the statue of Zeus is given as 40 feet when its height on scale model is given as 8 inches. Also to find the required scale factor between two heights.

Answer to Problem 26SR

Scale factor required is 1:60 or 60 only.

Explanation of Solution

Given information: The height of the statue of Zeus on scale model is 8 inches and its actual height is 40 feet.

Concept used:

Scale is actually a comparison between two quantities, that results the one unit of one quantity equals to how much unit of second quantity. Also, scale factor is the ratio between two corresponding given quantities. It is also used the following conversion formula:

1 feet= 12 inches

Calculation: As 40 feet $=40\times 12=480$ inches

So scale factor required $=\frac{\text{Actual height of statue}}{\text{Height of statue on scale model}}=\frac{480}{8}=\frac{60}{1}$

Based on above calculation, required scale factor is 1:60.