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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 40 m² and the large tin covers 60 m². (a) Percy publishes this chart showing the ar... 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 and large tins are of different widths. This representation can give the erroneous impression that the areas they cover are proportionate to the heights of the bars, which is not the case.
Step 2
Calculate the radius of the large tin.
Answer
To determine the radius of the large tin, we first calculate the volume of the standard tin:
The formula for the volume of a cylinder is given by:
Assuming both tins have the same height, the volume of the standard tin is:
The volume of the large tin is:
For the large tin, let the radius be r. Thus,
Setting the volumes equal gives:
This implies:
Thus,
r = rac{ ext{sqrt}(150)}{1} ext{ cm} \\ r ext{ is approximately } 12.247 ext{ cm.}