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A model railway is built using the scale 1 : 87 - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
A model railway is built using the scale 1 : 87. (a) On the model railway, the distance between the rails is 16.5mm. Calculate, in metres, the distance between the r... show full transcript
Worked Solution & Example Answer:A model railway is built using the scale 1 : 87 - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
Calculate, in metres, the distance between the rails for a full-size train.
Answer
To find the distance for a full-size train, we first calculate the actual distance using the scale.
Given that the scale is 1 : 87, this means that 1 unit on the model represents 87 units in reality.
The distance on the model is 16.5 mm. To convert this to metres, we first convert mm to m:
Next, we multiply by the scale factor:
Therefore, the distance between the rails for a full-size train is approximately 1.44 m.
Step 2
Is Trevor's calculation correct? Show how you decide.
Answer
To determine if Trevor's calculation of 334 cm³ is correct, we can compare his figure to the known volume of the full-size train carriage, which is 220 m³.
First, we need to convert 220 m³ into cm³:
Now, to find the corresponding volume of the model train carriage using the scale of 1 : 87:
Using the relationship:
ext{Model volume} = rac{ ext{Full-size volume}}{87^3}
Calculating:
= rac{220000000}{658503} ext{ cm³} \ ext{(approx)} = 334.26 ext{ cm³} $$ Trevor's calculation of 334 cm³ can be considered accurate to 3 significant figures. Thus, Trevor's calculation is correct.