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Let's solve the questions one by one based on the image you've uploaded.

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### (a) The length of the model is 22 cm. What is the length of the real aircraft in meters?

The model is built to a scale of 1:72, meaning that 1 unit of measurement on the model represents 72 units on the real aircraft.

- **Length of the model** = 22 cm
- **Scale** = 1:72

The length of the real aircraft can be calculated as:
\[
\text{Length of real aircraft} = \text{Length of model} \times 72
\]
\[
\text{Length of real aircraft} = 22 \, \text{cm} \times 72 = 1584 \, \text{cm}
\]
Since 1 meter = 100 cm, convert 1584 cm to meters:
\[
\text{Length of real aircraft} = \frac{1584 \, \text{cm}}{100} = 15.84 \, \text{m}
\]

So, the length of the real aircraft is **15.84 meters**.

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### (b) The real aircraft has a wingspan of 10.7 meters. What is the wingspan of the model, correct to the nearest centimeter?

To find the wingspan of the model, we divide the wingspan of the real aircraft by the scale factor (72).

- **Wingspan of the real aircraft** = 10.7 meters = 1070 cm
- **Scale** = 1:72

The wingspan of the model is:
\[
\text{Wingspan of model} = \frac{\text{Wingspan of real aircraft}}{72}
\]
\[
\text{Wingspan of model} = \frac{1070 \, \text{cm}}{72} \approx 14.86 \, \text{cm}
\]

Rounding to the nearest centimeter, the wingspan of the model is **15 cm**.

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### (c) The real aircraft can hold 8200 kg of fuel in its fuel tanks when full. Assuming the aircraft uses fuel at a constant rate of 40 kg/min, for how many minutes can the plane fly on a full tank of fuel?

To find the number of minutes the plane can fly, we divide the total fuel capacity by the rate of fuel consumption.

- **Fuel capacity** = 8200 kg
- **Fuel consumption rate** = 40 kg/min

The flight time is:
\[
\text{Flight time} = \frac{\text{Fuel capacity}}{\text{Fuel consumption rate}}
\]
\[
\text{Flight time} = \frac{8200 \, \text{kg}}{40 \, \text{kg/min}} = 205 \, \text{minutes}
\]

So, the plane can fly for **205 minutes** on a full tank of fuel.

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Do you want more details on any of these solutions? Here are five related questions to deepen your understanding:

1. How do we calculate scale ratios in models for other objects?
2. How would the length of the model change if the scale was 1:100 instead of 1:72?
3. What are some common applications of scale models in engineering and design?
4. If the fuel consumption rate increases to 50 kg/min, how will the flight time change?
5. What factors could affect the actual fuel consumption of a real aircraft?

**Tip**: Always double-check unit conversions when working with measurements in different units (e.g., cm to meters).

Tom builds a model of a fighter aircraft. The model is made to a scale of 1:72. The length of the model is 22 cm. What is the length of the real aircraft in meters? The real aircraft has a wingspan of 10.7 meters. What is the wingspan of the model, correct to the nearest centimeter? The real aircraft can hold 8200 kg of fuel in its fuel tanks when full. Assuming the aircraft uses fuel at a constant rate of 40 kg/min, for how many minutes can the plane fly on a full tank of fuel?

Learn how to solve problems involving scale models and unit conversions, including finding the length and wingspan of a real aircraft based on a model, and calculating flight time based on fuel consumption. This lesson covers key concepts for middle school students in Grades 6-8.

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