Question

The scale of a model airplane is 1:72.

If the wingspan on the model airplane is 7 1/2 inches, then the wingspan of the actual airplane is how many feet?

45 feet
9.6 feet
540 feet
72 feet

Answer 1

To find the wingspan of the actual airplane based on the scale model, we use the scale ratio and perform the following steps:

1. **Convert the wingspan of the model from inches to feet**:
The wingspan of the model airplane is \( 7 \frac{1}{2} \) inches.
First, convert this mixed number to an improper fraction:
\[
7 \frac{1}{2} = \frac{15}{2} \text{ inches}
\]
Now convert inches to feet by dividing by 12 (since there are 12 inches in a foot):
\[
\text{Wingspan in feet} = \frac{15/2}{12} = \frac{15}{24} = \frac{5}{8} \text{ feet}
\]

2. **Calculate the actual wingspan using the scale**:
The scale of the model airplane is 1:72, which means that 1 unit on the model corresponds to 72 units on the actual airplane.
To find the actual wingspan, we multiply the model's wingspan in feet by the scale factor:
\[
\text{Actual wingspan} = \text{Model wingspan} \times 72
\]
\[
\text{Actual wingspan} = \frac{5}{8} \text{ feet} \times 72
\]

3. **Simplify the calculation**:
\[
\frac{5 \times 72}{8} = \frac{360}{8} = 45 \text{ feet}
\]

Thus, the wingspan of the actual airplane is **45 feet**.