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Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place - OCR - GCSE Maths - Question 14 - 2018 - Paper 1
Question 14
Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place. A house is built using 4663 standard bricks. Joslin says Placed end to e... show full transcript
Worked Solution & Example Answer:Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place - OCR - GCSE Maths - Question 14 - 2018 - Paper 1
Step 1
Show that Joslin's statement is correct.
Answer
To determine whether the bricks placed end to end reach over 1 km, we first need to calculate the total length of the bricks.
- Calculate the length of one brick:
The length of one standard brick is 21.5 cm. - Calculate the total length of all bricks:
Total length = Number of bricks × Length of one brick
Total length = 4663 × 21.5 cm
Total length = 100,000.5 cm. - Convert the total length to kilometers:
100,000.5 cm = 1,000.005 m = 1 km (since 100 cm = 1 m). - Conclusion:
Therefore, 1,000.005 m exceeds 1 km, showing that Joslin's statement is indeed correct.
Step 2
Calculate the maximum number of standard bricks that the truck should be able to carry.
Answer
- Convert the truck's maximum load to kg:
The truck can carry 20 tonnes.
20 tonnes = 20,000 kg. - Calculate the number of bricks that can fit into this weight:
Maximum number of bricks = Total load / Weight of one brick
Maximum number of bricks = 20,000 kg / 2.8 kg
Maximum number of bricks = 7,142.857 (round down to 7142 bricks to the nearest whole number). - Conclusion:
The truck should be able to carry a maximum of 7142 standard bricks.
Step 3
Explain why your answer to (b)(i) may not be possible to achieve.
Answer
The answer to (b)(i) may not be possible to achieve due to several practical constraints:
- Truck Capacity: The actual space available in the truck may not accommodate all 7142 bricks, as they may not fit correctly due to their dimensions.
- Weight Limitations: Safety regulations may impose strict limits on how much cargo can be carried despite the weight calculations,
- Loading Issues: Issues with loading and securing the bricks safely in the truck may also prevent carrying the full calculated load.