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Why are tins of beans the size that they are?

Why are tins of beans the size that they are?. Are they the most efficient size they could be?. Task. Calculate the volume of a cylindrical food tin by any suitable method. Determine the optimal dimensions for a tin of the volume you calculated.

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Why are tins of beans the size that they are?

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  1. Why are tins of beans the size that they are? Are they the most efficient size they could be?

  2. Task Calculate the volume of a cylindrical food tin by any suitable method. Determine the optimal dimensions for a tin of the volume you calculated.

  3. Draw round the base of your tin on squared paper and measure the diameter, e.g. Or draw round the base on blank paper and use circle geometry to find the centre and hence a diameter, e.g. X Step 1 Calculate the volume of your tin What measurements will you need to make? What steps will you take to ensure that your measurements are as accurate as possible? Hint

  4. A = X A = Replace V with the value for the volume of your tin. X Step 2 Write down an expression for the surface area of a cylinder in terms of r and h. Hint By using the calculated volume of your tin, determine an expression for the surface area of your tin in terms of r. Hint

  5. Differentiate your expression for surface area A, then solve A’ = 0 to find the value of r that minimises A. X Step 3 Calculate the dimensions, rand h, that minimise the surface area of your tin and hence find the minimum surface area required for a tin of your volume. Hint Did the manufacturer of your tin optimise the amount of material used? If not, can you think of reasons why not?

  6. X actual – optimal × 100% optimal Step 4 Calculate the percentage difference between the actual surface area of your tin and the optimal surface area of a tin with the same volume. Hint

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