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Percy sells paint in standard tins and large tins - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Question 18
Percy sells paint in standard tins and large tins. The standard tin covers 40m² and the large tin covers 60m². (a) Percy publishes this chart showing the area that ... show full transcript
Worked Solution & Example Answer:Percy sells paint in standard tins and large tins - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Step 1
Explain why the chart is misleading.
Answer
The chart is misleading because the bars representing the standard tin and the large tin are of different widths. This causes the visual interpretation of the areas covered to be inaccurate, making the large tin appear to cover more area than it actually does.
Step 2
Calculate the radius of the large tin.
Answer
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Calculate the volume of the standard tin:
- The volume of a cylinder is given by the formula:
Given the standard tin has a radius (r) of 10 cm:
V_{standard} = rac{22}{7} (10^2) h
Simplifying,
V_{standard} = rac{2200}{7} h
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The volume of the large tin is 50% more than that of the standard tin:
V_{large} = V_{standard} imes 1.5 = rac{2200}{7} h imes 1.5 = rac{3300}{7} h
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Let the radius of the large tin be R:
V_{large} = rac{22}{7} R^2 h
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Equating both volumes:
rac{3300}{7} h = rac{22}{7} R^2 h
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Canceling h and rearranging gives:
ightarrow R = ext{sqrt}(150) ightarrow R ext{approximately } 12.25 ext{ cm}$$
Thus, the radius of the large tin is approximately 12.25 cm.