Numeracy Higher November 2022 Unit 1 Q7
7. Nia saw this bottle rack in her local hotel.
Nia decides to make a smaller bottle rack in the same style.
The front view of her bottle rack is shown below.
Nia made the rack from bending a long sheet of metal.
It has straight sections, each of length 6·6 cm.
It also has curved sections that are all arcs of a circle with radius 4·5 cm and sector angles of 120º or 240º.
Diagram not drawn to scale
Calculate the length of the sheet of metal that Nia needed for her design.
Give your answer in terms of \(\pi\), in its simplest form.
You must show all your working. [5]
Length of metal sheet needed = …………… cm
| Scheme | Marks | Comments |
|---|---|---|
| Use of \(\dfrac{240}{360}\) × π × 2 × 4.5 OR \(\dfrac{120}{360}\) × π × 2 × 4.5 or their equivalents | B1 | Allow use of π = 3.1 to 3.142 for B and M marks only 6π OR 3π |
| (Length of metal sheet needed =) 4 × \(\dfrac{240}{360}\)×π×2×4.5 + 2 × \(\dfrac{120}{360}\)×π×2×4.5 or equivalent OR 5 × \(\dfrac{240}{360}\)×π×2×4.5 or equivalent | M2 | Implies the previous B1 Could come from adding all the angles (=1200) M1 for
|
| + 5 × 6.6 | m1 | Depends on at least M1 previously awarded |
| = 30π + 33 or 3(10π + 11) (cm) | A1 | CAO Mark final answer Answer space takes precedence If no marks awarded, SC2 for an answer of 15π + 33 (cm) from using a diameter of 4.5 (cm) or SC1 for a full method that would arrive at an answer of 15π + 33 (cm) from using a diameter of 4.5 (cm), but with error/s in accuracy |