Higher June 2019 Paper 3 Q6
6 Jeremy has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.6 m and a height of 1.8 m.
Jeremy has 7 tins of paint.
Each tin of paint covers 5 m2
Has Jeremy got enough paint to cover completely the 3 tanks?
You must show how you get your answer. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| No Supported | P1 | for finding the area of a circle eg \(\pi \times 0.8^2\) (= 2.01...) |
| P1 | for finding the curved surface area eg \(2\pi \times 0.8 \times 1.8\) (= 9.047…) | |
| P1 | for use of the coverage information with an area eg \(\text{``}2.01\ldots\text{''} \div 5\) (= 0.402…) or \(\text{``}4.02\ldots\text{''} \div 5\) (= 0.804…) or \(\text{``}9.047\ldots\text{''} \div 5\) (= 1.8095…) or \(\text{``}11.058\text{''} \div 5\) (= 2.2116..) or \(\text{``}13.069\ldots\text{''} \div 5\) (= 2.6138…) OR for process to find total coverage for comparison eg \(5 \times 7\ (= 35)\) | |
| P1 | (dep P1) for finding total surface area for 3 tanks eg [total surface area] \(\times 3\) (= 39.2…) OR for complete process to find the number of tins needed for total area of 3 tanks eg \(\text{``}13.069\ldots\text{''} \times 3 \div 5\) (= 7.84…) OR for complete process to find coverage needed from each tin eg \(\text{``}13.069\ldots\text{''} \times 3 \div 7\) (= 5.6...) | |
| C1 | for conclusion “No” supported by accurate figures eg 8 tins or 7.84 (> 7) or 39.2 > 35 or 5.6 (> 5) |
Additional guidance
Must be area of circle and not part of a volume, eg \(\pi r^2 h\)
May be seen as \(2\pi r^2\)
May be seen from \(2\pi rh\) or from \(\pi dh\)
Accept numbers without working written to no less than 2dp
Do not award if a volume has been used as part of the calculation.
An independent mark for 5 × 7
[total surface area] must come from the addition of two attempts at area, but not from volume.
Clear statement that there is not enough paint supported by correct figures for comparison.
NB: 2.6 × 3 = 9 tins needed is inaccurate
8 or 7.84 tins is sufficient without restating the 7, 5.6 m2 is sufficient without restating the 5 but 39.2 and 35 are needed for comparison.
A statement of “No, 8 tins” alone gets 0 marks without supporting working.