olds 175 ml of water.","location":"specification"}]},{"type":"text","order":4,"title":"State final answer","content":"Since we need to find how many cups can be **completely** filled, we must round down to the nearest whole number.\n\n$$\\text{Number of fully filled cups} = 9$$ A1","highlights":[{"text":"completely filled","location":"specification"}]}]},{"id":"73ace6b3-dae5-4c1d-a1c3-856a60d0e3fe:totalcups","label":"Total Cups First","steps":[{"type":"text","order":0,"title":"Calculate the total volume","content":"First, we find the total volume of the rectangular container when it is completely full. \n\nUsing the formula for the volume of a rectangular prism:\n$$\\text{Volume} = \\text{length} \\times \\text{width} \\times \\text{height}$$\n\nSubstituting the dimensions from the diagram:\n$$\\text{Total Volume} = 15 \\text{ cm} \\times 12 \\text{ cm} \\times 14 \\text{ cm} = 2520 \\text{ cm}^3$$\n\nSince $1 \\text{ cm}^3 = 1 \\text{ ml}$, the total capacity of the container is $2520 \\text{ ml}$."},{"type":"text","order":1,"title":"Find max cups capacity","content":"Now, we calculate how many cups could be filled if the container were completely full. Each cup holds $175 \\text{ ml}$.\n\n$$\\text{Total Cups (if full)} = \\frac{2520 \\text{ ml}}{175 \\text{ ml}} = 14.4 \\text{ cups}$$","highlights":[{"text":"Each cup holds 175 ml of water.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=fraction}{\\frac{2}{3}} \\text{ of the container is full}$"},{"latex":"$$\\text{Actual Cups} = \\htmlData{anchor=fraction-mult}{\\frac{2}{3}} \\times \\htmlData{anchor=max-cups}{14.4}$"},{"latex":"$$\\phantom{\\text{Actual Cups}} = 9.6 \\text{ cups}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"fraction"},{"color":"amber","style":"box","anchor":"max-cups"}],"connections":[{"to":"fraction-mult","from":"fraction","color":"sky","label":"fraction full","style":"solid"}]},"order":2,"title":"Scale by fraction full","description":"Since the container is only $\\frac{2}{3}$ full, we scale the maximum number of cups by $\\frac{2}{3}$."},{"type":"text","order":3,"title":"Find completely filled cups","content":"We need to find how many cups can be **completely** filled.\n\nSince $9.6$ cups can be filled, we round down to the nearest whole number because the $10^{\\text{th}}$ cup will only be $0.6$ (or $60\\%$) full.\n\nTherefore, the number of completely filled cups is **$9$**.","highlights":[{"text":"completely filled","location":"specification"}]}]}],"generatedAt":"2026-06-13T01:41:32.121Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":8}},{"id":"74346c3c-5512-4ea4-8d36-8f6248deb60b","revisionId":"2db239d9-c338-4dbf-9a1e-9ecb7f05f543","questionNumber":"13","questionType":"LA","specification":"![Diagram of a triangular prism.](https://assets.mathsgenie.co.uk/questions/14316cc9-dbe2-4ad9-b661-4c33c640ce8f.png)\n\nThe diagram shows a triangular prism. The cross-section of the prism is a right angled triangle.","difficulty":3,"difficultyBand":"hard","totalMarks":5,"sourceTitle":"Volume of a Prism","calculatorUse":"non_calc","parts":[{"id":"82850f98-bbb2-414f-896a-18c78925f94b","label":"0","content":"Calculate the volume of the prism.","markscheme":"- Uses Pythagoras to find height: $x^2 + 12^2 = 13^2$ M1\n- $x = \\sqrt{169 - 144} = 5$ A1\n- Area of cross section = $\\frac{5 \\times 12}{2} = 30 \\text{ cm}^2$ M1\n- Volume = $30 \\times 8$ M1\n- Final answer = $240 \\text{ cm}^3$ A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Applies Pythagoras' theorem to find the missing side of the triangle.","code":"M"},{"id":"p2","marks":1,"description":"Correctly calculates the height of the triangle as 5.","code":"A"},{"id":"p3","marks":1,"description":"Calculates the area of the triangular cross-section.","code":"M"},{"id":"p4","marks":1,"description":"Multiplies the cross-sectional area by the leng

Volume of a Prism

Question 35

Volume of a Prism Questions

Volume of a Prism

Question 35

Volume of a Prism Questions