A stationery firm prints square labels. The cost \(C\) pence varies as the square of the side \(s\) cm. A label of side 4 cm costs 12 pence. Work out the co...
Question 1 Report
A stationery firm prints square labels. The cost \(C\) pence varies as the square of the side \(s\) cm. A label of side 4 cm costs 12 pence.
- Work out the cost of a label of side 6 cm. (2)
Answer Details
Varying as the square of a quantity means \(C \propto s^2\), that is \(C = ks^2\) for a fixed constant \(k\).
- Substitute the known label: \(12 = k \times 4^2 = 16k\), so \(k = \frac{12}{16} = 0.75\). [1]
- For a side of 6 cm, \(C = 0.75 \times 6^2 = 0.75 \times 36 = 27\), so the label costs 27 pence. [1]
The relationship makes sense in context, since the amount of ink and paper depends on the area of the label, and the area of a square of side \(s\) is \(s^2\).
The side increases by a factor of \(\frac{6}{4} = 1.5\), so the cost increases by a factor of \(1.5^2 = 2.25\), and \(12 \times 2.25 = 27\) pence. Multiplying the cost by 1.5 instead, giving 18 pence, is the usual error and ignores the squaring.
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