:"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A=\\dfrac{1}{2}(a+b)h$"},{"latex":"$$A=\\dfrac{1}{2}\\htmlData{anchor=sides}{\\color{@sky}{(2+6)}}\\times\\htmlData{anchor=height}{\\color{@orange}{3}}$"},{"latex":"$$A=\\htmlData{anchor=area}{\\color{@green}{12\\text{ m}^2}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"sides"},{"color":"orange","style":"text-color-with-background","anchor":"height"},{"color":"green","style":"text-color-with-background","anchor":"area"}]},"order":1,"title":"Find cross-section area","description":"Use the trapezium area formula, then substitute the two parallel sides and the perpendicular distance. This earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V=A\\times l$"},{"latex":"$$V=\\htmlData{anchor=used_area}{\\color{@sky}{12}}\\times\\htmlData{anchor=used_length}{\\color{@orange}{10}}$"},{"latex":"$$V=\\htmlData{anchor=volume}{\\color{@green}{120\\text{ m}^3}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"used_area"},{"color":"orange","style":"text-color-with-background","anchor":"used_length"},{"color":"green","style":"text-color-with-background","anchor":"volume"}]},"order":2,"title":"Multiply by length","description":"A prism's volume is its cross-sectional area multiplied by its length. Writing 12 x 10 earns the second M1 mark, and the correct final answer of 120 cubic metres earns the A1 mark."}]}],"generatedAt":"2026-07-20T10:35:10.230Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"cd1d4c6d-951d-43fc-af28-69810f56ed1e","revisionId":"a0b2889e-b761-4411-83d0-0e8b55eb02f3","questionNumber":null,"questionType":"LA","specification":"A glass prism has a cross-section in the shape of a right-angled triangle. The hypotenuse of the triangle is $10 \\text{ cm}$ and its height is $6 \\text{ cm}$. The length of the prism is $12 \\text{ cm}$.","difficulty":3,"difficultyBand":"hard","totalMarks":5,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"3ee79456-09df-4125-b1ec-a8f1e9c75962","label":"a","content":"Calculate the volume of the prism.","markscheme":"- Uses Pythagoras to find the missing side (base): $x^2 + 6^2 = 10^2$ M1\n- $x = \\sqrt{100 - 36} = 8$ A1\n- Area of cross-section = $\\frac{6 \\times 8}{2} = 24 \\text{ cm}^2$ M1\n- Volume = $24 \\times 12$ M1\n- Final answer = $288 \\text{ cm}^3$ A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Correct Pythagoras setup: $10^2 - 6^2$.","code":"M"},{"id":"p2","marks":1,"description":"Finds the missing triangle side length as 8.","code":"A"},{"id":"p3","marks":1,"description":"Calculation of the area of the triangular face.","code":"M"},{"id":"p4","marks":1,"description":"Calculation of the volume using Area × length.","code":"M"},{"id":"p5","marks":1,"description":"Final numerical value for volume.","code":"A"}],"finalAnswers":["288 \\text{ cm}^3","288"],"generatedAt":"2026-05-06T14:05:40.142Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"pythagoras_then_volume","label":"Pythagoras then volume","steps":[{"type":"text","order":0,"title":"Identify the triangle","content":"The prism has a triangular cross-section. The hypotenuse is $10\\text{ cm}$ and the perpendicular height is $6\\text{ cm}$, so use Pythagoras to find the missing base before finding the triangle's area.","highlights":[{"text":"The hypotenuse of the triangle is $10 \\text{ cm}$ and its height is $6 \\text{ cm}$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=pythagoras}{\\color{@sky}{x^2+6^2=10^2}}$"},{"latex":"$$\\htmlData{anchor=rearranged}{\\color{@sky}{x^2=10^2-6^2}}$"},{"latex":"$$\\htmlData{anchor=evaluated}{\\color{@amber}{x^2=100-36}}$"},{"latex":"$$\\htmlData{anchor=answer}{\\col

Volume of a Prism

Question 16

Volume of a Prism Questions

Volume of a Prism

Question 16

Volume of a Prism Questions