Higher November 2018 Paper 3 Q15
15 A company makes two types of lampshade using fabric on wire frames.
Lampshade A
Fabric is used to make the curved surface of a cylinder.
The cylinder has radius 8 cm and height 22 cm
Lampshade B
Fabric is used to make the four triangular faces of a pyramid.
Each triangular face has base 15 cm and perpendicular height 24 cm
Not drawn accurately
| Cost of fabric | £400 per square metre |
| Other costs for A | £3.50 per lampshade |
| Other costs for B | £7.50 per lampshade |
Work out the ratio cost of one lampshade A : cost of one lampshade B
Give your answer in the form \(\quad n : 1\) [5 marks]
| Answer | Mark | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| \(2 \times \pi \times 8 \times 22\) or \(352\pi\) or [1105, 1106] | M1 | Area of lampshade A oe \(2 \times \pi \times 0.08 \times 0.22\) or \(0.0352\pi\) or [0.1105, 0.1106] | ||||||
| \(4 \times \dfrac{1}{2} \times 15 \times 24\) or 720 | M1 | Area of lampshade B oe \(4 \times \dfrac{1}{2} \times 0.15 \times 0.24\) or 0.072 | ||||||
| M1dep |
| ||||||
| \(\text{their } 14.08\pi + 3.50\) or [47.7, 47.74] and \(\text{their } 28.8(0) + 7.5(0)\) or 36.3(0) | M1dep | dep on M3 and method for fabric cost for both lampshades correct | ||||||
| 1.3(1…) : 1 or 1.32 : 1 | A1 |
Additional guidance
| 1 : 1.3(1…) or 1 : 1.32 | M4A0 |