4-4-13-volume-of-a-prism/questions","formulaUrl":null,"initialIndex":12,"initialQuestionWindow":[{"id":"e3bdc9a3-7f6a-4b2d-af1a-f23591d50e83","revisionId":"561016a1-77e0-4025-a581-9c8f157c53b8","questionNumber":"2","questionType":"LA","specification":"![Diagram of a triangular prism with dimensions 3 cm, 4 cm, 5 cm, and 8 cm.](https://assets.mathsgenie.co.uk/questions/26d57a2a-9874-465f-8cae-21f16184e067.png)\n\nThe diagram shows a triangular prism. The cross-section of the prism is a right angled triangle.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Volume of a Prism","calculatorUse":"non_calc","parts":[{"id":"8a7f6745-2e03-42b5-aebf-73d40a699b71","label":"0","content":"Calculate the volume of the prism.","markscheme":"- Area of cross section = $\\frac{3 \\times 4}{2} = 6 \\text{ cm}^2$ M1\n- Volume = $6 \\times 8$ M1\n- Final answer = $48 \\text{ cm}^3$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the area of the triangular cross-section using base and height.","code":"M"},{"id":"p2","marks":1,"description":"Multiplies the cross-sectional area by the length (8 cm).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 48.","code":"A"}],"finalAnswers":["48"],"generatedAt":"2026-05-06T11:03:31.583Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"cross_section_area","label":"Cross-section area method","steps":[{"type":"text","order":0,"title":"Identify the cross-section","content":"The repeated cross-section is the right-angled triangle at the end of the prism. Its perpendicular base and height are $4\\text{ cm}$ and $3\\text{ cm}$. The $5\\text{ cm}$ side is the sloping side, so it is not needed for the area."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A_{\\triangle}=\\htmlData{anchor=area_calculation}{\\color{@sky}{\\dfrac{1}{2}\\times 4\\times 3}}$"},{"latex":"$$A_{\\triangle}=\\htmlData{anchor=area_result}{\\color{@green}{6\\text{ cm}^2}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"area_calculation"},{"color":"green","style":"text-color","anchor":"area_result"}],"connections":[{"to":"area_result","from":"area_calculation","color":"sky","label":"calculate"}]},"order":1,"title":"Find triangle area","description":"Use the right-angled triangle's perpendicular sides, 3 cm and 4 cm, as the base and height. Writing 3 × 4 ÷ 2 earns the first method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V=\\htmlData{anchor=volume_product}{\\color{@sky}{6\\times8}}$"},{"latex":"$$V=\\htmlData{anchor=volume_answer}{\\color{@green}{48\\ \\mathrm{cm}^{3}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"volume_product"},{"color":"green","style":"text-color","anchor":"volume_answer"}],"connections":[{"to":"volume_answer","from":"volume_product","color":"sky","label":"calculate"}]},"order":3,"title":"Calculate prism volume","description":"Multiply the cross-section area by the prism's length. Writing 6 × 8 earns the second method mark (M1), and 48 cm³ earns the accuracy mark (A1). Volume must be given in cubic units, so use cm³."}]}],"generatedAt":"2026-07-19T02:08:19.278Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"1b9d49a6-4ae5-4317-b7b5-499f0bff966e","revisionId":"8d01854a-05ff-497a-b3f6-011d7123c7d7","questionNumber":null,"questionType":"LA","specification":"A gold bar in the shape of a cuboid has dimensions $10\\text{ cm}$, $3\\text{ cm}$, and $x\\text{ cm}$. The volume of the bar is $105\\text{ cm}^3$.","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"4f1e8174-a6a5-4ddf-a6a6-a656a522dfd7","label":"a","content":"Calculate the value of $x$.","markscheme":"- $10 \\times 3 \\times x = 105$ M1\n- $30x = 105 \\implies x = 3.5$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","

Volume of a Prism

Question 4

Volume of a Prism Questions

Volume of a Prism

Question 4

Volume of a Prism Questions