A corner shop is painting a shop-front display board. The board is a rectangle \(2.4\) m by \(1.5\) m. A circular mirror of radius \(0.4\) m is fixed at the...

The area to be painted is the rectangular board's area with the circular mirror's area removed, and the number of tins needed must always be rounded up, since part of a tin cannot be bought.

(a) The board's area is \( 2.4 \times 1.5 = 3.6 \ \text{m}^2 \) [1 mark].

(b) The mirror's area is \( \pi \times 0.4^2 = 0.503 \ \text{m}^2 \) to 3 significant figures [1 mark].

(c) Subtracting the unrounded mirror area from the board's area gives the area to be painted: \( 3.6 - 0.5027\ldots = 3.0973\ldots \), which rounds to \( 3.10 \ \text{m}^2 \) to 3 significant figures [1 mark].

(d) Dividing the unrounded painted area by the coverage of one tin gives \( 3.0973\ldots \div 1.2 = 2.58\ldots \) tins [1 mark]. Since only whole tins can be bought and 2 tins would not be enough to cover the area, this must be rounded up to 3 tins [1 mark].

(e) Buying 3 tins individually costs \( 3 \times £14.50 = £43.50 \), whereas the multi-buy pack of 3 costs \( £38 \), a saving of \( £43.50 - £38 = £5.50 \). Since the multi-buy pack is cheaper for the exact number of tins needed, the shop should use it [2 marks].

Rounding the number of tins down to 2 (the usual rule for 3 significant figures) would leave part of the board unpainted; "number of tins" questions always round up to the next whole tin, regardless of how close the decimal is to the lower whole number.