Foundation June 2019 Paper 3 Q29
29 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 \(2\pi \times 0.8 \times 1.8\ (= 9.047\ldots)\) | |
| P1 | for use of the coverage information with an area eg \(\text{``}2.01\ldots\text{''} \div 5\ (= 0.402\ldots)\) or \(\text{``}4.02\ldots\text{''} \div 5\ (= 0.804\ldots)\) or \(\text{``}9.047\ldots\text{''} \div 5\ (= 1.8095\ldots)\) or \(\text{``}11.058\text{''} \div 5\ (= 2.2116..)\) or \(\text{``}13.069\ldots\text{''} \div 5\ (= 2.6138\ldots)\) 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] \({} \times 3\ (= 39.2\ldots)\) OR for complete process to find the number of tins needed for total area of 3 tanks eg \(\text{``}13.069\text{''}... \times 3 \div 5\ (= 7.84...)\) OR for complete process to find coverage needed from each tin eg \(\text{``}13.069\text{''}... \times 3 \div 7\ (= 5.6...)\) | |
| C1 | for conclusion “No” supported by accurate figures eg 8 tins or 7.84 (\(\gt 7\)) or \(39.2 \gt 35\) or 5.6 (\(\gt 5\)) |
Additional guidance
For the first P1: Must be area of circle and not part of a volume, eg \(\pi r^2 h\)
May be seen as \(2\pi r^2\)
For the second P1: May be seen from \(2\pi rh\) or from \(\pi dh\)
For the third P1: 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 \(5 \times 7\)
For the fourth P1: [total surface area] must come from the addition of two attempts at area, but not from volume.
For the C1: Clear statement that there is not enough paint supported by correct figures for comparison.
NB: \(2.6 \times 3 = 9\) 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.