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bg-background","children":["$","$L3a",null,{"backHref":"/gcse/maths/edexcel/questions","basePath":"/gcse/maths/edexcel/grade-4-4-13-volume-of-a-prism/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":11,"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/question-image-redraws/sol-max-v1/e3bdc9a3-7f6a-4b2d-af1a-f23591d50e83/image-1-cc6253297299fb5827a29e31.svg)\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","isCalculation":true,"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"},"tableImages":[],"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":{"percent":70},"walkthroughVideo":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","isCalculation":true,"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","marks":1,"description":"Correct expression for volume set equal to 105.","code":"M"},{"id":"p2","marks":1,"description":"Correct calculation of x.","code":"A"}],"finalAnswers":["3.5"],"generatedAt":"2026-05-06T14:05:31.229Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":{"methods":[{"id":"4f1e8174-a6a5-4ddf-a6a6-a656a522dfd7:algebraic","label":"Algebraic Equation","steps":[{"type":"text","order":0,"title":"Recall the volume formula","content":"To find the missing dimension, we use the formula for the volume ($V$) of a cuboid:\n\n$$V = \\text{length} \\times \\text{width} \\times \\text{height}$$\n\nIn this problem, the dimensions are given as $10\\text{ cm}$, $3\\text{ cm}$, and $x\\text{ cm}$, and the total volume is $105\\text{ cm}^3$.","highlights":[{"text":"dimensions 10 cm, 3 cm, and x cm","location":"specification"},{"text":"volume of the bar is 105 cm3","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Volume} = \\text{length} \\times \\text{width} \\times \\text{height}$"},{"latex":"$$\\htmlData{anchor=vol-eq}{\\color{@sky}{105}} = \\htmlData{anchor=dim-eq}{\\color{@amber}{10 \\times 3 \\times x}}$"}],"highlights":[{"color":"sky","style":"box","anchor":"vol-eq"},{"color":"amber","style":"box","anchor":"dim-eq"}],"connections":[{"to":"dim-eq","from":"vol-eq","color":"sky","label":"Substitute given values","style":"solid"}]},"order":1,"title":"Set up the equation","description":"Substitute the known values into the cuboid volume formula to set up our algebraic equation. This earns the first mark (M1)."},{"type":"text","order":2,"title":"Simplify and solve for x","content":"Now, let's simplify the right side of our equation:\n\n$$10 \\times 3 \\times x = 30x$$\n\nSo the equation becomes:\n\n$$30x = 105$$\n\nTo find $x$, divide both sides by $30$:\n\n$$\\begin{aligned} x &= \\frac{105}{30} \\\\ x &= 3.5 \\end{aligned}$$\n\nThus, the value of $x$ is $3.5\\text{ cm}$. This step gives us the final mark (A1)."}]},{"id":"4f1e8174-a6a5-4ddf-a6a6-a656a522dfd7:arithmetic","label":"Step-by-Step Arithmetic","steps":[{"type":"text","order":0,"title":"Identify the known dimensions","content":"A cuboid has three dimensions: length, width, and height. In this problem, we are given two of these dimensions:\n- Length = $10\\text{ cm}$\n- Width = $3\\text{ cm}$\n\nWe also know the total volume of the cuboid is $105\\text{ cm}^3$.","highlights":[{"text":"10\\text{ cm}","location":"specification"},{"text":"3\\text{ cm}","location":"specification"},{"text":"105\\text{ cm}^3","location":"specification"}]},{"type":"text","order":1,"title":"Calculate the face area","content":"First, we calculate the area of the cross-section (or face) with the two known dimensions:\n\n$$\\text{Area} = 10\\text{ cm} \\times 3\\text{ cm} = 30\\text{ cm}^2$$\n\nThis represents the area of one of the faces of the gold bar. Finding this step helps set up our final division."},{"type":"text","order":2,"title":"Calculate the missing dimension","content":"The volume of a cuboid is calculated by multiplying the area of this face by the remaining dimension, $x$:\n\n$$\\text{Volume} = \\text{Area} \\times x$$\n\nTo find the missing dimension $x$, we divide the total volume by the area of the known face we just calculated:\n\n$$x = \\frac{105}{30}$$\n\n$$x = 3.5\\text{ cm}$$\n\nThis simple step-by-step arithmetic confirms that the third dimension is $3.5\\text{ cm}$.","calculator":[{"gdc":{"expression":"105 / 30","instructions":"Type 105 / 30 and press ENTER."},"ti84":{"expression":"105 / 30","instructions":"Type 105 / 30 and press ENTER."},"desmos":{"expression":"105 / 30","instructions":"Type 105 / 30 in the input field."},"description":"Perform the division on a calculator to find the decimal value."}],"highlights":[{"text":"x","location":"specification"}]}]}],"generatedAt":"2026-06-12T11:00:20.402Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":80},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/1b9d49a6-4ae5-4317-b7b5-499f0bff966e.mp4","durationSeconds":65,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/1b9d49a6-4ae5-4317-b7b5-499f0bff966e.jpg"}},{"id":"680e47b5-142e-4334-bc42-fddef0fd28b5","revisionId":"91a20788-aee2-4f96-a550-7eb7b3c0f2e8","questionNumber":null,"questionType":"LA","specification":"A cube has side lengths of 4 cm.","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"2d706984-a36d-40ce-b6b8-54210170fc4d","label":"a","content":"Work out the total volume of 3 of these cubes.","markscheme":"- Volume of one cube = $4 \\times 4 \\times 4 = 64 \\text{ cm}^3$ M1\n- Volume of three cubes = $64 \\times 3 = 192 \\text{ cm}^3$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculation of the volume of a single cube ($4^3$ or $4 \\times 4 \\times 4$).","code":"M"},{"id":"p2","marks":1,"description":"Total volume for 3 cubes.","code":"A"}],"finalAnswers":["192","192 cm^3"],"generatedAt":"2026-05-06T14:05:29.890Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"volume_then_multiply","label":"Find one, then multiply","steps":[{"type":"text","order":0,"title":"Recall the formula","content":"The volume of a cube is found by multiplying its side length by itself three times. Volume is measured in cubic centimetres, written as $\\text{cm}^3$.","highlights":[{"text":"A cube has side lengths of 4 cm.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V=\\htmlData{anchor=product}{\\color{@sky}{4\\times4\\times4}}$"},{"latex":"$$V=\\htmlData{anchor=one_volume}{\\color{@green}{64\\text{ cm}^3}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"product"},{"color":"green","style":"text-color-with-background","anchor":"one_volume"}],"connections":[{"to":"one_volume","from":"product","color":"green","label":"calculate"}]},"order":1,"title":"Find one cube","description":"Use length × width × height. Writing this correct calculation earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$V_{\\text{total}}=\\htmlData{anchor=three_product}{\\color{@sky}{64\\times3}}$"},{"latex":"$$V_{\\text{total}}=\\htmlData{anchor=total_volume}{\\color{@green}{192\\text{ cm}^3}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"three_product"},{"color":"green","style":"text-color-with-background","anchor":"total_volume"}],"connections":[{"to":"total_volume","from":"three_product","color":"green","label":"calculate"}]},"order":2,"title":"Find three cubes","description":"Multiply the volume of one cube by the number of cubes. The correct total earns A1."}]}],"generatedAt":"2026-07-20T10:55:03.484Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"2d706984-a36d-40ce-b6b8-54210170fc4d:one_cube_then_multiply","label":"Volume of One Cube First","steps":[{"type":"text","order":0,"title":"Understand the goal","content":"We need to find the total volume of $3$ identical cubes. \n\nOur approach will be:\n1. Calculate the volume of a single cube.\n2. Multiply that volume by $3$ to find the total volume.","highlights":[{"text":"total volume of 3 of these cubes","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Volume of one cube} = \\htmlData{anchor=side-length}{\\color{@sky}{s}}^3$"},{"latex":"$$\\phantom{\\text{Volume of one cube}} = \\htmlData{anchor=side-val}{\\color{@sky}{4}}^3$"},{"latex":"$$\\phantom{\\text{Volume of one cube}} = \\color{@sky}{4} \\times \\color{@sky}{4} \\times \\color{@sky}{4} = \\htmlData{anchor=vol-val}{\\color{@pink}{64}} \\text{ cm}^3$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"side-length"},{"color":"sky","style":"text-color","anchor":"side-val"},{"color":"pink","style":"box","anchor":"vol-val"}],"connections":[{"to":"side-val","from":"side-length","color":"sky","label":null,"style":"solid"}]},"order":1,"title":"Calculate volume of one cube","description":"Each cube has side lengths of $4\\text{ cm}$. The volume $V$ of a cube with side length $s$ is given by the formula:\n\n$$V = s^3$$\n\nCalculating this gives us the volume of one cube: $64\\text{ cm}^3$ (this earns the first method mark **M1**)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Total Volume} = \\htmlData{anchor=vol-one}{\\color{@pink}{64}} \\times \\htmlData{anchor=num-cubes}{\\color{@teal}{3}}$"},{"latex":"$$\\phantom{\\text{Total Volume}} = \\htmlData{anchor=total-val}{\\color{@purple}{192}} \\text{ cm}^3$"}],"highlights":[{"color":"pink","style":"text-color","anchor":"vol-one"},{"color":"teal","style":"text-color","anchor":"num-cubes"},{"color":"purple","style":"box","anchor":"total-val"}],"connections":[{"to":"total-val","from":"vol-one","color":"pink","label":null,"style":"solid"}]},"order":2,"title":"Calculate total volume","description":"Since we have $3$ identical cubes, we multiply the volume of a single cube by $3$ to find the total volume:\n\n$$64 \\times 3 = 192 \\text{ cm}^3$$\n\nThis final answer earns the accuracy mark **A1**."}]},{"id":"2d706984-a36d-40ce-b6b8-54210170fc4d:single_expression","label":"Single Expression Calculation","steps":[{"type":"text","order":0,"title":"Set up the expression","content":"To find the total volume of three cubes directly, we can write a single mathematical expression.\n\nFirst, we know the volume of one cube with side length $s = 4\\text{ cm}$ is given by:\n$$\\text{Volume of one cube} = 4 \\times 4 \\times 4$$\n\nSince we want the total volume of $3$ of these identical cubes, we multiply this volume by $3$:\n$$\\text{Total Volume} = 3 \\times (4 \\times 4 \\times 4)$$","highlights":[{"text":"side lengths of 4 cm","location":"specification"},{"text":"total volume of 3 of these cubes","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Total Volume} = 3 \\times \\htmlData{anchor=cube-vol}{\\color{@sky}{(4 \\times 4 \\times 4)}}$"},{"latex":"$$\\phantom{\\text{Total Volume}} = 3 \\times \\htmlData{anchor=cube-val}{\\color{@sky}{64}}$"},{"latex":"$$\\phantom{\\text{Total Volume}} = 192 \\text{ cm}^3$"}],"highlights":[{"color":"sky","style":"box","anchor":"cube-vol"},{"color":"sky","style":"text-color","anchor":"cube-val"}],"connections":[{"to":"cube-val","from":"cube-vol","color":"sky","label":"calculate cube volume first","style":"solid"}]},"order":1,"title":"Evaluate the expression","description":"We evaluate the volume of one cube first, then multiply by 3 to find the total volume."},{"type":"text","order":2,"title":"State final answer","content":"The total volume of the 3 cubes is **$192\\text{ cm}^3$**.\n\n**Marks Distribution:**\n* **M1**: Setting up the calculation for the volume of one cube ($4 \\times 4 \\times 4$ or $64$)\n* **A1**: Finding the correct total volume ($192\\text{ cm}^3$)"}]},{"id":"2d706984-a36d-40ce-b6b8-54210170fc4d:repeated_addition","label":"Repeated Addition of Volumes","steps":[{"type":"text","order":0,"title":"Calculate volume of one cube","content":"A cube has equal lengths for its width, depth, and height. The formula for the volume of a single cube is:\n\n$$\\text{Volume} = \\text{side} \\times \\text{side} \\times \\text{side}$$\n\nGiven that the side length is $4\\text{ cm}$:\n\n$$\\text{Volume of one cube} = 4\\text{ cm} \\times 4\\text{ cm} \\times 4\\text{ cm} = 64\\text{ cm}^3$$\n\nCalculating this volume correctly earns you the first mark (\\mathbf{M1}).","highlights":[{"text":"side lengths of 4 cm","location":"specification"}]},{"type":"text","order":1,"title":"Use repeated addition","content":"To find the total volume of $3$ of these identical cubes, we can add the volume of one cube three times:\n\n$$\\text{Total Volume} = 64\\text{ cm}^3 + 64\\text{ cm}^3 + 64\\text{ cm}^3$$","highlights":[{"text":"total volume of 3 of these cubes","location":"specification"}]},{"type":"text","order":2,"title":"Calculate the final sum","content":"Let's perform the addition:\n\n$$64 + 64 + 64 = 192\\text{ cm}^3$$\n\nThis final answer of $192\\text{ cm}^3$ earns you the second mark 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of a Prism","topicId":"a2c45350-2311-4854-9d87-ef997348f7a0","topicSidebar":"$L3b","topicSlug":"grade-4-4-13-volume-of-a-prism","topicTitle":"Volume of a Prism"}]}],"$L3c","$L3d"]}]

Volume of a Prism

Question 4

Volume of a Prism Questions

Volume of a Prism

Question 4

Volume of a Prism Questions