Foundation November 2022 Paper 3 Q24
24 Karina has 4 tanks on her tractor.
Each tank is a cylinder with diameter 80 cm and height 160 cm.
The 4 tanks are to be filled completely with a mixture of fertiliser and water.
The fertiliser has to be mixed with water in the ratio \(1 : 100\) by volume.
Karina has 32 litres of fertiliser.
1 litre = 1000 cm\(^3\)
Has Karina enough fertiliser for the 4 tanks?
You must show how you get your answer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Yes (supported) | P1 | for a process to find the volume of 1 tank eg \(\pi \times 40^2 \times 160\ (= 804247.7… \text{ or } 804.2... \text{ or } 256000\pi)\) |
| P1 | for complete process to find the volume of 4 tanks, [volume of tank] \(\times\ 4\) eg \(\pi \times 40^2 \times 160 \times 4\ (= 3216990.8… \text{ or } 3216.9... \text{ or } 1024000\pi)\) or for process to find volume of fertiliser available per tank eg \(32 \times 1000 \div 4\ (= 8000)\) | |
| P1 | for a process to find the amount of mixture for 1 tank eg [volume of tank] \(\div\ 101\ (= 7962.8...)\) or 4 tanks \((= 31851.3…)\) OR for a process to find volume of mixture that 32 litres of fertiliser will make eg \(32000 \times 101\ (= 3232000)\) or \(32 \times 101\ (= 3232)\) | |
| C1 | for Yes supported by correct figures shown eg a comparable figure in the range 31.8 to 31.9 (litres) or in the range 31800 to 31900 with 32000 (cm³) or in the range 3216 to 3217 with 3232 (litres) or in the range 3216000 to 3217000 with 3232000 (cm³) or in the range 7958 to 7963 with 8000 (cm³) |
Additional guidance
First P1: Could be truncated or rounded
Second P1: For this mark [volume of tank] must come from a calculation involving \(\pi\), \(r^2\), \(h\)
Third P1: For this mark [volume of tank] must come from a calculation involving \(\pi\), \(r^2\), \(h\) or be stated as their volume
C1: There are other possible pairs of values which can be used in the comparison