s or uses the pressure-force-area relationship $A = \\frac{F}{p}$ M1\n- Converts the force from kilonewtons to Newtons: $72\\text{ kN} = 72\\,000\\text{ N}$ B1\n- Substitutes the values to find the numerical area: $A = \\frac{72\\,000}{3.2 \\times 10^7} = 0.00225$ M1\n- States the final answer in standard form with the correct unit: $2.25 \\times 10^{-3}\\text{ m}^2$ A1","marks":4,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"pressure_formula","label":"Rearrange the pressure equation","steps":[{"type":"text","order":1,"title":"Choose the relationship","content":"Pressure is force per unit area. Rearranging $p=\\dfrac{F}{A}$ for the cross-sectional area gives\n\n$$A=\\dfrac{F}{p}$$\n\nWriting this relationship earns the first method mark (M1).","highlights":[{"text":"Calculate the cross-sectional surface area of the piston.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"F = 72\\,\\mathrm{kN}"},{"latex":"F = \\htmlData{anchor=forceN}{72\\,000\\,\\mathrm{N}}"}],"highlights":[{"color":"amber","style":"box","anchor":"forceN"}]},"order":2,"title":"Convert the force","description":"Convert kilonewtons to newtons. The prefix kilo means one thousand, so 72 kilonewtons is 72 000 newtons. Writing this correct conversion earns B1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"A = \\frac{F}{p}"},{"latex":"A = \\frac{\\htmlData{anchor=force}{72\\,000\\,\\mathrm{N}}}{\\htmlData{anchor=pressure}{3.2 \\times 10^{7}\\,\\mathrm{Pa}}}"},{"latex":"\\htmlData{anchor=result}{A = 0.00225\\,\\mathrm{m}^{2}}"}],"highlights":[{"color":"green","style":"box","anchor":"result"}]},"order":4,"title":"Substitute the values","description":"Substitute 72 000 N for the force and 3.2 × 10^7 Pa for the pressure. Obtaining 0.00225 m² earns the substitution and calculation M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=decimal}{A = 0.00225\\,\\mathrm{m}^{2}}"},{"latex":"\\htmlData{anchor=final}{A = 2.25 \\times 10^{-3}\\,\\mathrm{m}^{2}}"}],"highlights":[{"color":"green","style":"box","anchor":"final"}],"connections":[{"to":"final","from":"decimal","color":"green","label":"standard form"}]},"order":5,"title":"Write standard form","description":"Move the decimal point three places to the right: 0.00225 becomes 2.25 × 10^-3. Writing 2.25 × 10^-3 m² in standard form with the unit earns A1."}]}],"generatedAt":"2026-07-22T11:46:37.871Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"a3ffacea-0430-4fd5-9daa-bbfadc464804","revisionId":"6b42c0d1-f81f-45d4-8ee2-4568fa1fcaaa","questionNumber":null,"questionType":"LA","specification":"A rectangular fuel tank on an aircraft is filled with biofuel. The weight of the liquid fuel exerts a pressure on the flat bottom of the tank.\n\n![A rectangular tank with base dimensions labeled 0.40 m and 0.75 m.](https://assets.mathsgenie.co.uk/aqa-qb/dc2954a7-510a-4244-a58e-19057640c475.png)\n\nThe pressure exerted by the fuel on the bottom of the tank is $4200\\text{ Pa}$.","difficulty":3,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"846192fd-bf45-44b2-bf77-bae57497c99c","label":null,"content":"Calculate the force of the fuel on the bottom of the tank.","markscheme":"- Recalls or uses the relation $\\text{pressure} = \\frac{\\text{force}}{\\text{area}}$ or $F = P \\times A$ M1\n- Calculates the area of the rectangular bottom of the tank: $0.40\\text{ m} \\times 0.75\\text{ m} = 0.30\\text{ m}^2$ M1\n- Evaluates the force as $4200\\text{ Pa} \\times 0.30\\text{ m}^2 = 1260\\text{ N}$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"pressure_area","label":"Use pressure and area","steps":[{"type":"text","order":0,"title":"Choose the relationship","content":"Pressure is force per unit area, so use\n\n$$P=\\frac{F}{A}$$\n\nRearrange this to make force the subject: $F

Pressure and pressure differences in fluids (physics only)

Question 13

Pressure and pressure differences in fluids (physics only) Questions

Pressure and pressure differences in fluids (physics only)

Question 13

Pressure and pressure differences in fluids (physics only) Questions