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A transport lorry consists of a cab and a trailer - OCR - GCSE Maths - Question 13 - 2019 - Paper 4
Question 13
A transport lorry consists of a cab and a trailer. The trailer has a volume of 90m³. Alfie makes a model of this lorry using a scale of 1 : 72. Work out the volume ... show full transcript
Worked Solution & Example Answer:A transport lorry consists of a cab and a trailer - OCR - GCSE Maths - Question 13 - 2019 - Paper 4
Step 1
Work out the volume of the trailer in Alfie’s model, giving your answer in cm³.
Answer
To find the volume of the trailer in Alfie's model, we first need to convert the original volume from cubic meters to cubic centimeters.
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The original volume of the trailer is 90 m³. We know that:
1 m³ = 1,000,000 cm³
Therefore,
90 m³ = 90 imes 1,000,000 cm³ = 90,000,000 cm³.
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Since the scale of the model is 1 : 72, we need to find the volume of the model. Since volume scales with the cube of the linear dimensions, we will apply the scale factor cubed:
Volume of model = Volume of trailer × (Scale factor)³
= 90,000,000 cm³ × (1/72)³
= 90,000,000 cm³ × (1/373248)
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Calculating the above:
= 241.41 cm³ (approx).
Therefore, the volume of the trailer in Alfie’s model is approximately 241.41 cm³.
Step 2
In how many different ways can Alfie paint his model lorry?
Answer
To find the total number of ways Alfie can paint his model lorry, we need to consider the choices for painting the cab, the trailer, and then the name on the trailer.
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Alfie can choose from 8 colours for the cab.
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For the trailer, he can also choose from 8 colours, but it must be different from the colour selected for the cab. Thus, he has:
7 choices left for the trailer.
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For painting his name, he can choose from any of the 7 colours that are different from the trailer colour:
6 choices available for the name colour (different from the trailer colour).
Combining these choices together:
Total ways = (Ways to paint cab) × (Ways to paint trailer) × (Ways to paint name)
Total ways = 8 × 7 × 6 = 336. Therefore, Alfie can paint his model lorry in 336 different ways.