Solve.
27. A historical diorama (3d scene) is being built using a 1 : 24 scale. Determine the correct height in inches of the model of a 6ft. tall individual. 28. A 1 : 24 model of a car is 7 1/4 in. long. How long is the car? 29. Model trains often use the HO scale, which is approximately 1 : 87. What is the actual length in feet of a locomotive whose model is 8 in. long? 30. Determine the length, to the nearest inch, of a 1 : 265 scale model of the Titanic, which was 883 ft. 9 in. long.
27. To find the height of the model of a 6ft. tall individual, we need to multiply 6 by the scale factor of 24.
6 x 24 = 144
Therefore, the correct height in inches of the model of a 6ft. tall individual is 144 inches.
28. To find the length of the car, we need to multiply the given length of the model by the scale factor of 24.
7 1/4 x 24 = 174
Therefore, the length of the car is 174 inches.
29. To find the actual length of the locomotive, we need to multiply the length of the model by the scale factor of 87.
8 x 87 = 696
Therefore, the actual length of the locomotive is 696 inches or 58 feet.
30. To find the length of the 1 : 265 scale model of the Titanic, we need to divide the actual length of the Titanic by the scale factor of 265.
883 ft. 9 in. = 10,603 inches
10,603 ÷ 265 = 40
Therefore, the length of the 1 : 265 scale model of the Titanic is 40 inches.
To solve these scale problems, you'll need to use the concept of proportionality. The ratio in the scale is used to compare the dimensions of the model to the actual object. Here's how you can solve each question:
27. To determine the correct height of the model of a 6 ft. tall individual, you'll need to use the given scale of 1:24. You can set up the proportion as:
1 inch / 24 inches = x inches / 72 inches (6 ft. in inches)
Now, solve for x using cross multiplication:
24 * x = 1 * 72
x = 72 / 24
x = 3
So, the correct height of the model of a 6 ft. tall individual is 3 inches.
28. For this question, you're given the length of the 1:24 model car, which is 7 1/4 inches. You need to find the actual length of the car. Using the same approach as before, set up the proportion as:
1 inch / 24 inches = 7.25 inches / x inches
Cross multiply:
24 * 7.25 = 1 * x
x = 24 * 7.25
x = 174 inches
So, the actual length of the car is 174 inches.
29. In this question, you are dealing with the HO scale of approximately 1:87. You need to find the actual length of the locomotive when the model is 8 inches long. Set up the proportion:
1 inch / 87 inches = 8 inches / x inches
Using cross multiplication:
87 * 8 = 1 * x
x = 87 * 8
x = 696 inches
To convert the inches to feet, divide by 12:
696 / 12 = 58 feet
So, the actual length of the locomotive is 58 feet.
30. In this question, you have a 1:265 scale model of the Titanic, and you need to find the length in inches. Set up the proportion as:
1 inch / 265 inches = x inches / 883.75 inches (convert ft. to inches: 883 ft. 9 in. = 883 * 12 + 9)
Using cross multiplication:
265 * x = 1 * 883.75
x = 883.75 / 265
x ≈ 3.33
Therefore, the length of the 1:265 scale model of the Titanic is approximately 3.33 inches to the nearest inch.
27. To determine the height of the model of a 6ft. tall individual in inches, we need to multiply the height by the scale factor.
Scale factor: 1 : 24
Height of the individual: 6 ft.
To convert feet to inches, we multiply by 12:
Height in inches = 6 ft * 12 in/ft = 72 in
Now, we multiply the height in inches by the scale factor:
Model height = 72 in * 1/24 = 3 in
Therefore, the correct height of the model of a 6ft. tall individual is 3 inches.
28. To find the length of the car, we will multiply the given length of the model by the scale factor.
Scale factor: 1 : 24
Length of the model: 7 1/4 in.
To add fractions, we need a common denominator:
The length of the model can be written as 7 1/4 = 7 + 1/4 = 28/4 + 1/4 = 29/4
Now, we multiply the length of the model by the scale factor:
Length of the car = (29/4 in) * 24 = 696/4 in
Simplifying the fraction:
Length of the car = 174 in
Therefore, the car is 174 inches long.
29. To find the actual length in feet of the locomotive, we multiply the length of the model by the scale factor.
Scale factor: 1 : 87
Length of the model: 8 in.
Length of the locomotive = 8 in * 87 = 696 in
To convert inches to feet, we divide by 12:
Length of the locomotive = 696 in / 12 = 58 ft
Therefore, the actual length of the locomotive is 58 feet.
30. To determine the length of the 1:265 scale model of the Titanic, we need to multiply the actual length by the scale factor.
Scale factor: 1 : 265
Actual length of the Titanic: 883 ft. 9 in.
We need to convert the length of the Titanic to inches:
Actual length = 883 ft * 12 in/ft + 9 in = 10595 in
Now, we multiply the actual length by the scale factor:
Length of the model = 10595 in / 265 = 40 in
Therefore, the length of the 1:265 scale model of the Titanic is 40 inches.