The wingspan of a Boeing 747-400 is 64.4 metres.
a. If a scale model is built to the scale 1:20, what would the wingspan of the model be in
centimetres?
b. If the wingspan of another model is 53 cm, find the scale of the model in the form 1:x.
64.4/20 * 100 cm
a. To find the wingspan of the model in centimeters, we need to convert the meters to centimeters and apply the scale factor of 1:20.
The conversion factor from meters to centimeters is 100, so we can multiply the wingspan in meters by 100 to get the wingspan in centimeters.
Wingspan of the model = Wingspan of the Boeing 747-400 x Scale factor
= 64.4 meters x 100 cm/meter (conversion factor) x 1/20
= 3220 cm
Therefore, the wingspan of the model would be 3220 centimeters.
b. To find the scale of the other model in the form 1:x, we can use the given wingspan of the model and the wingspan of the Boeing 747-400.
Scale of the model = Wingspan of the Boeing 747-400 / Wingspan of the model
= 64.4 meters / 53 cm
= (64.4 meters * 100 cm/meter) / 53 cm
= 6440 cm / 53 cm
= 121.51
Therefore, the scale of the model is approximately 1:121.51.
To solve both parts of the question, we need to understand the concept of scale. Scale is a ratio that compares the measurements of the model to the actual object. In this case, the scale is given as 1:20.
a. To find the wingspan of the model in centimeters, we need to convert the actual wingspan, given in meters, to centimeters. Since 1 meter equals 100 centimeters, the actual wingspan is 64.4 x 100 = 6440 centimeters.
Next, we need to apply the scale of 1:20 to find the wingspan of the model. To do this, we divide the actual wingspan by the scale factor (20):
6440 cm / 20 = 322 cm
Therefore, the wingspan of the model is 322 centimeters.
b. To find the scale of the other model, given its wingspan of 53 cm, we need to compare it to the actual wingspan using a scale factor of 1:x.
Let's assume the scale factor is 1:x. We can write the proportion as:
1:x = 64.4 m : 53 cm
To solve this proportion, we need to make sure the units are consistent. Since both measurements are in centimeters, we need to convert the actual wingspan, given in meters, to centimeters:
64.4 m = 64.4 x 100 cm = 6440 cm
Now the proportion becomes:
1:x = 6440 cm : 53 cm
To find x, we can cross-multiply and solve for x:
6440 cm * 1 = 53 cm * x
6440 = 53x
x = 6440 / 53
Using a calculator, we find that x ≈ 121.51.
Therefore, the scale of the model in the form 1:x is approximately 1:121.51.