To find the wingspan of the actual airplane based on the scale model, we use the scale ratio and perform the following steps:
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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):
\[ \text{Wingspan in feet} = \frac{15/2}{12} = \frac{15}{24} = \frac{5}{8} \text{ feet} \] -
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: \[ \text{Actual wingspan} = \text{Model wingspan} \times 72 \] \[ \text{Actual wingspan} = \frac{5}{8} \text{ feet} \times 72 \] -
Simplify the calculation:
\[ \frac{5 \times 72}{8} = \frac{360}{8} = 45 \text{ feet} \]
Thus, the wingspan of the actual airplane is 45 feet.