Higher November 2020 Paper 2 Q9
9 The diagram shows a solid cylinder with radius 3 m.
Diagram NOT accurately drawn
The volume of the cylinder is \(72\pi\) m3
Calculate the total surface area of the cylinder.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\pi \times 3^2 \times h = 72\pi\) oe | M1 |
| \(h = 72\pi \div (\pi \times 3^2)\) oe or \(h = 8\) | M1 |
| \(2 \times \pi \times 3^2\) (= \(18\pi\) or 56.54...) or \(2 \times \pi \times 3 \times\) “8” oe (= \(48\pi\) or 150 - 151) | M1 |
| \(2 \times \pi \times 3^2 + 2 \times \pi \times 3 \times\) “8” oe (= \(66\pi\)) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 207 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: Allow use of 3.14... or \(\dfrac{22}{7}\) for \(\pi\) and use of 226... for \(72\pi\)
M1: method to isolate \(h\) (may be seen in several stages)
M1: method to find the area of the two circles or curved surface area – use of their \(h\), dep on 1st M1
(NB may get this mark for total area of 2 circles with no previous marks awarded)
M1: method to find total surface area ft their \(h\) dep on 1st M1, including intention to add, to find the total surface area
A1: accept 207-208