Volume

OCR

GCSE

Volume quantification requires the selection and application of specific geometric formulae for prisms, pyramids, spheres, and composite solids. Candidates must calculate cross-sectional areas accurately and apply dimensional multipliers, distinguishing between perpendicular height and slant height where necessary. The study extends to the manipulation of algebraic expressions to derive missing dimensions and the rigorous conversion of metric units, including the relationship between cubic centimetres and litres.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Subtopics in this area

Volume

What You Need to Demonstrate

Key skills and knowledge for this topic

Award M1 for correct substitution of numerical values into the specific volume formula (e.g., π × r² × h for cylinders)
Award M1 for decomposing composite solids into constituent parts and showing the summation of their individual volumes
Award B1 for stating correct units (e.g., cm³, m³) when the question explicitly requests them or provides a blank answer line without units
Award A1 for answers given in terms of π where 'exact value' is specified, or for correct rounding to the required degree of accuracy
Award M1 for correct calculation of the cross-sectional area (e.g., 0.5 × base × height for triangular prisms)
Award M1 for multiplying the calculated cross-sectional area by the correct length/depth
Award B1 for stating the correct units (e.g., cm³ or m³) when explicitly requested or as part of communication marks
Award M1 for correct substitution of values into the formulae for spheres or cones (Higher Tier)

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have correctly selected the formula, but check your input values—did you use diameter instead of radius?"
"Well done on the calculation; to secure the final mark, ensure your answer is rounded to 3 significant figures as requested."
"You missed the method mark here because you didn't show the unsimplified substitution step before writing the answer."
"For this similarity question, remember that if the length scale factor is k, the volume scale factor must be k³."

Marking Points

Key points examiners look for in your answers

Award M1 for correct substitution of numerical values into the specific volume formula (e.g., π × r² × h for cylinders)
Award M1 for decomposing composite solids into constituent parts and showing the summation of their individual volumes
Award B1 for stating correct units (e.g., cm³, m³) when the question explicitly requests them or provides a blank answer line without units
Award A1 for answers given in terms of π where 'exact value' is specified, or for correct rounding to the required degree of accuracy
Award M1 for correct calculation of the cross-sectional area (e.g., 0.5 × base × height for triangular prisms)
Award M1 for multiplying the calculated cross-sectional area by the correct length/depth
Award B1 for stating the correct units (e.g., cm³ or m³) when explicitly requested or as part of communication marks
Award M1 for correct substitution of values into the formulae for spheres or cones (Higher Tier)
Award A1 for the final answer within the specified range of accuracy (usually ±0.1)

Examiner Tips

Expert advice for maximising your marks

💡When a question asks for an answer in terms of π, treat π as an algebraic variable throughout your working and do not convert it to a decimal.
💡For 'Show that' questions involving volume, you must explicitly write down the substitution step (e.g., V = π × 3² × 10) before the final answer to secure the method mark.
💡Check the dimensions of the shape immediately; if a slant height (l) is given for a cone but the formula requires vertical height (h), use Pythagoras' theorem first.
💡Always state the formula used before substituting values; this secures a method mark even if the subsequent calculation contains an arithmetic error
💡When dealing with composite solids, clearly label the calculation for each component (e.g., 'Volume of Cylinder' and 'Volume of Hemisphere') to maximize partial credit
💡For 'Show that' questions involving volume, you must show the unrounded value first before giving the final answer to the required accuracy

Common Mistakes

Pitfalls to avoid in your exam answers

Omitting the 1/3 multiplier when calculating the volume of cones or pyramids, treating them effectively as cylinders or prisms
Confusing diameter with radius, particularly when squaring the value in the formula V = πr²h
Failing to convert units prior to calculation, such as multiplying dimensions in cm by dimensions in mm
Incorrectly applying the volume scale factor as k rather than k³ when dealing with similar shapes
Confusing surface area formulae with volume formulae, particularly calculating 2πr for area of a circle instead of πr²
Neglecting the factor of 1/3 when calculating volumes of pyramids and cones
Failing to convert units to a consistent standard before calculation (e.g., mixing cm and mm)
Premature rounding of intermediate values (e.g., rounding π or the cross-section area) leading to an inaccurate final answer

Study Guide Available

Comprehensive revision notes & examples

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Key Terminology

Essential terms to know

Formulae for prisms (cuboids, cylinders, triangular prisms)

Formulae for tapered solids (cones, pyramids, spheres)

Volume of composite solids and frustums

Dimensional analysis and unit conversion

Algebraic manipulation of volume formulae

Volume of right prisms (cuboids, cylinders, triangular prisms)

Volume of tapered solids (cones, pyramids, spheres)

Compound measures involving density, mass, and volume

Volume scale factors in similar shapes ($k^3$)

Likely Command Words

How questions on this topic are typically asked

Calculate

Show that

Work out

Estimate

Compare

Determine

Solve

Practical Links

Related required practicals

•{"code":"Density/Mass/Volume","title":"Material Properties","relevance":"Calculating volume to determine mass or density of engineering components"}
•{"code":"Flow Rates","title":"Capacity and Time","relevance":"Using volume calculations to solve rates of flow problems (e.g., filling a tank)"}

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