Clarissa makes a scale model of the Titanic.

* The actual Titanic was 175 feet tall.
* Clarissa's model is 35 inches tall.

What is the scale factor comparing Clarissa's model to the actual Titanic? 7.MGSR.2.2
12 inches : 36 feet
1 inch : 35 feet
12 inches : 3 feet
1 Inch : 5 feet

1 answer

To find the scale factor comparing Clarissa's model to the actual Titanic, we first need to convert the heights into the same units. We will convert the actual height of the Titanic (in feet) into inches, since Clarissa's model height is given in inches.

  1. Convert the actual Titanic height:
  • 1 foot = 12 inches
  • The actual Titanic's height = 175 feet × 12 inches/foot = 2100 inches
  1. The height of Clarissa's model is 35 inches.

Now, we can set up the scale factor as the ratio of the height of the model to the height of the actual Titanic: \[ \text{Scale factor} = \frac{\text{Height of model}}{\text{Height of actual Titanic}} = \frac{35 \text{ inches}}{2100 \text{ inches}} \]

  1. Simplifying the ratio: \[ \text{Scale factor} = \frac{35}{2100} = \frac{1}{60} \]

Now we will convert this scale factor into a more interpretable format. From our original ratio: \[ 1 \text{ inch (in the model)} : 60 \text{ inches (in actual size)} \] To convert inches back to feet in the actual size, we know:

  • 60 inches = 60 / 12 feet = 5 feet

Thus, the scale factor can be represented as: \[ 1 \text{ inch} : 5 \text{ feet} \]

Therefore, the correct answer is: 1 inch : 5 feet.