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$96 \\text{ cm}^2$.","difficulty":2,"difficultyBand":"medium","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"e73b505c-7a82-448b-b4d3-e24d94a29833","label":"0","content":"Work out the volume of the cube.","markscheme":"- Area of one face = $96 \\div 6 = 16 \\text{ cm}^2$ M1\n- Side length = $\\sqrt{16} = 4 \\text{ cm}$ M1\n- Volume = $4 \\times 4 \\times 4$ M1\n- Final answer = $64 \\text{ cm}^3$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Finds the area of one face by dividing the total surface area by 6.","code":"M","acceptable":["$$96 \\div 6 = 16 \\text{ cm}^2$","Area of one face = $16 \\text{ cm}^2$"]},{"id":"p2","marks":1,"description":"Finds the side length by taking the square root of the area of one face.","code":"M","acceptable":["$$\\sqrt{16} = 4 \\text{ cm}$","Side length = $4 \\text{ cm}$"]},{"id":"p3","marks":1,"description":"Uses the cube volume formula with the correct side length.","code":"M","acceptable":["$$4 \\times 4 \\times 4$","$$4^3$"]},{"id":"p4","marks":1,"description":"Gives the correct volume with appropriate units.","code":"A","acceptable":["$$64 \\text{ cm}^3$","64 cm³"]}],"finalAnswers":["64 cm^3"],"generatedAt":"2026-09-22T14:55:48.261Z","modelVersion":"gpt-5.6-sol"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"2763eb0d-5630-419f-906e-b5d2076d2775","revisionId":"2a4e141c-561f-4626-8abf-a5771c6f01bb","questionNumber":"9","questionType":"LA","specification":"![A 3D diagram of a cube with side lengths labeled 3 cm.](https://assets.mathsgenie.co.uk/booklet/09a93a52ea5cb3615e726921beb4423c42f123f163e29d6458bcaf1f6a7e5a1a.jpg)\n\nHere is a cube.","difficulty":1,"difficultyBand":"medium","tier":null,"totalMarks":2,"sourceTitle":"Volume of a Prism","calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"c9c2ecec-0958-4c0d-91de-3fb05295df25","label":"0","content":"Work out the volume of five of these cubes.","markscheme":"- Volume of one cube = $3 \\times 3 \\times 3 = 27 \\text{ cm}^3$ M1\n- Volume of five cubes = $27 \\times 5 = 135 \\text{ cm}^3$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates the volume of a single cube ($3^3$).","code":"M"},{"id":"p2","marks":1,"description":"Multiplies the single volume by 5 to get 135.","code":"A"}],"finalAnswers":["135"],"generatedAt":"2026-05-06T11:03:31.583Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"volume_then_multiply","label":"Find one, then five","steps":[{"type":"text","order":0,"title":"Identify every dimension","content":"A cube has equal length, width and height. The diagram gives a side length of $3\\text{ cm}$, so all three dimensions are $3\\text{ cm}$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V=\\color{@sky}{\\htmlData{anchor=one_calc}{3\\times3\\times3}}$"},{"latex":"$$V=\\color{@green}{\\htmlData{anchor=one_volume}{27\\text{ cm}^3}}$"}],"connections":[{"to":"one_volume","from":"one_calc","color":"green","label":"multiply"}]},"order":1,"title":"Find one cube","description":"Multiply length, width and height. Writing this calculation earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V_{\\text{five}}=\\color{@sky}{\\htmlData{anchor=five_calc}{27\\times5}}$"},{"latex":"$$V_{\\text{five}}=\\color{@green}{\\htmlData{anchor=five_volume}{135\\text{ cm}^3}}$"}],"connections":[{"to":"five_volume","from":"five_calc","color":"green","label":"multiply"}]},"order":2,"title":"Find five cubes","description":"There are five identical cubes, so multiply the volume of one cube by five. The correct final value with cubic units earns the A1 mark."}]}],"generatedAt":"2026-07-19T06:59:06.299Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"c9c2ecec-0958-4c0d-91de-3fb05295df25:single_cube_first","label":"Volume of One Cube First","steps":[{"type":"text","order":0,"title":"Calculate volume of one cube","content":"To find the volume of a single cube, we multiply its length, width, and height. Since it is a cube, all its side lengths are equal to $3\\text{ cm}$:\n\n$$\\text{Volume of one cube} = 3\\text{ cm} \\times 3\\text{ cm} \\times 3\\text{ cm} = 27\\text{ cm}^3$$\n\nFinding the volume of one cube correctly awards you the first method mark (**M1**).","highlights":[{"text":"cube with side lengths labeled 3 cm","location":"specification"}]},{"type":"text","order":1,"title":"Multiply by five","content":"Now that we know one cube has a volume of $27\\text{ cm}^3$, we can find the total volume of five identical cubes by multiplying this value by $5$:\n\n$$\\text{Total Volume} = 27\\text{ cm}^3 \\times 5 = 135\\text{ cm}^3$$\n\nThis final step awards you the accuracy mark (**A1**).","highlights":[{"text":"five of these cubes","location":"specification"}]}]},{"id":"c9c2ecec-0958-4c0d-91de-3fb05295df25:combined_cuboid","label":"Combined Cuboid Method","steps":[{"type":"text","order":0,"title":"Visualize the combined cuboid","content":"Instead of finding the volume of one cube and multiplying by $5$, we can imagine placing all $5$ cubes side-by-side in a row.\n\nSince each cube has side lengths of $3\\text{ cm}$:\n- The height of the combined shape is $3\\text{ cm}$.\n- The width of the combined shape is $3\\text{ cm}$.\n- The total length of the $5$ cubes placed end-to-end is:\n $$3\\text{ cm} \\times 5 = 15\\text{ cm}$$\n\nThis forms one large cuboid with dimensions $15\\text{ cm} \\times 3\\text{ cm} \times 3\\text{ cm}$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V = \\htmlData{anchor=length}{\\color{@sky}{\\text{length}}} \\times \\htmlData{anchor=width}{\\color{@amber}{\\text{width}}} \\times \\htmlData{anchor=height}{\\color{@purple}{\\text{height}}}$"},{"latex":"$$V = \\htmlData{anchor=len-val}{\\color{@sky}{15}} \\times \\htmlData{anchor=wid-val}{\\color{@amber}{3}} \\times \\htmlData{anchor=hgt-val}{\\color{@purple}{3}}$"},{"latex":"$$V = 135\\text{ cm}^3$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"length"},{"color":"amber","style":"text-color","anchor":"width"},{"color":"purple","style":"text-color","anchor":"height"}],"connections":[{"to":"len-val","from":"length","color":"sky","label":null,"style":"solid"},{"to":"wid-val","from":"width","color":"amber","label":null,"style":"solid"},{"to":"hgt-val","from":"height","color":"purple","label":null,"style":"solid"}]},"order":1,"title":"Calculate the total volume","description":"Now, we can find the volume ($V$) of this combined cuboid directly by multiplying its length, width, and height."},{"type":"text","order":2,"title":"State the final answer","content":"The total volume of the five cubes is:\n\n$$\\mathbf{135\\text{ cm}^3}$$\n\n*(Note: On the markscheme, you receive **1 method mark** for showing the equivalent dimensions/multiplication step, and **1 accuracy mark** for the correct final answer of $135$)*"}]}],"generatedAt":"2026-06-12T12:23:48.439Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"gcse_maths__ocr","summaries":[{"id":"2a3d6ef8-7586-4251-b376-479b6c5e2648","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"39d12c3d-1888-4b48-9f69-f3b6610e7922","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"4da8cb24-c090-43a7-b535-165a4c41fabd","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4f03c9d8-7eb2-4eeb-8fa0-ce52a230b18f","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"55a41e1f-7543-4946-b6ab-75e7458be993","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6c952b0d-2df7-424c-8086-875862299314","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"71b53c09-b0c8-4ea7-8626-33136bdd30dd","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"77033a42-e7d5-48fb-9a7c-ec235b856206","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"88de3212-895c-47eb-8f56-b2476b4a4401","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c2393301-475b-4606-9953-c751685316a6","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"fe63963c-39f7-435f-9d1d-9313a8cb3f54","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"e3bdc9a3-7f6a-4b2d-af1a-f23591d50e83","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"07c7dcc9-dfef-4bf9-984f-c0d0f7a50cbd","difficultyBand":"hard","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"1b9d49a6-4ae5-4317-b7b5-499f0bff966e","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"3152fde1-8c6f-4e83-be4e-fba0d6f2844a","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"50d2b4da-cd7b-4bce-8e2e-5abadb0e6c27","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"64368a2b-b3e9-4a32-89ca-c0e104f3e07d","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"680e47b5-142e-4334-bc42-fddef0fd28b5","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"847534f8-290a-4c7d-b4f4-166770d3de0f","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9336bb0c-c7e5-48e7-b73d-e22714f98800","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"b96d6755-3297-417d-8be9-977ce421f624","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"bacb2956-7bcb-4c2d-8afd-5b95e5d69b87","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c555987c-c080-4533-9961-96e80d57a281","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"cad3b5be-0f5a-4684-8348-ec032c77518f","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"cd1d4c6d-951d-43fc-af28-69810f56ed1e","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"80d48b64-4705-41c9-88b2-6a21087401ed","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"05b0e3ec-ddac-425c-b622-e848c7791d0a","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"091f0946-b5cf-4925-b259-060766025b7a","difficultyBand":"medium","calculatorUse":"non_calc","totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"1e0e2d20-6ff2-4484-94df-487db19798c3","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"2be6ecf7-3406-4880-a8ac-36709b363713","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"556c525e-a528-4735-b563-f03b0f1dba34","difficultyBand":"hard","calculatorUse":"non_calc","totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"5b5b9f51-38d1-4715-b3ed-47b492315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of a Prism","topicId":"1ad5fa15-564d-4fe0-acf6-1b9e746be924","topicSidebar":"$L3b","topicSlug":"grade-4-4-13-volume-of-a-prism","topicTitle":"Volume of a Prism"}]}],"$L3c","$L3d"]}]

Volume of a Prism

Question 13

Volume of a Prism Questions

Volume of a Prism

Question 13

Volume of a Prism Questions