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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
    7 主题
  6. Combined-And-Conditional-Probability Aqa Higher
    3 主题
  7. Tree-Diagrams Aqa Higher
    1 主题
  8. Simple-Probability-Diagrams Aqa Higher
    3 主题
  9. Transformations Aqa Higher
    5 主题
  10. Vectors Aqa Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
    4 主题
  13. Pythagoras-And-Trigonometry Aqa Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
    5 主题
  16. Volume-And-Surface-Area Aqa Higher
    3 主题
  17. Circles-Arcs-And-Sectors Aqa Higher
    2 主题
  18. Area-And-Perimeter Aqa Higher
    4 主题
  19. Circle-Theorems Aqa Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Aqa Higher
    2 主题
  24. Standard-And-Compound-Units Aqa Higher
    5 主题
  25. Direct-And-Inverse-Proportion Aqa Higher
    2 主题
  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
    3 主题
  28. Sequences Aqa Higher
    4 主题
  29. Transformations-Of-Graphs Aqa Higher
    2 主题
  30. Graphing-Inequalities Aqa Higher
    2 主题
  31. Solving-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
    2 主题
  34. Equation-Of-A-Circle Aqa Higher
    2 主题
  35. Functions Aqa Higher
    3 主题
  36. Forming-And-Solving-Equations Aqa Higher
    3 主题
  37. Graphs-Of-Functions Aqa Higher
    6 主题
  38. Linear-Graphs Aqa Higher
    4 主题
  39. Coordinate-Geometry Aqa Higher
    4 主题
  40. Iteration Aqa Higher
    1 主题
  41. Simultaneous-Equations Aqa Higher
    2 主题
  42. Quadratic-Equations Aqa Higher
    4 主题
  43. Linear-Equations Aqa Higher
    1 主题
  44. Algebraic-Proof Aqa Higher
    1 主题
  45. Rearranging-Formulas Aqa Higher
    2 主题
  46. Algebraic-Fractions Aqa Higher
    4 主题
  47. Completing-The-Square Aqa Higher
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  48. Factorising Aqa Higher
    6 主题
  49. Expanding-Brackets Aqa Higher
    3 主题
  50. Algebraic-Roots-And-Indices Aqa Higher
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  51. Using-A-Calculator Aqa Higher
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  52. Surds Aqa Higher
    2 主题
  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
    3 主题
  55. Introduction Aqa Higher
    7 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
    4 主题
  57. Percentages Aqa Higher
    3 主题
  58. Fractions Aqa Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Aqa Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
    4 主题
  61. Number-Operations Aqa Higher
    10 主题
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Exam code:8300

Problem-solving with volumes

What is problem-solving?

  • Problem-solving, usually has two key features:

    • A question is given as a real-life scenario

      • eg. The volume of water in a swimming pool…

    • There is usually more than one topic of maths you will need in order to answer the question

      • eg. Volume and money

What are common problems that involve volume?

  • Volume is a commonly used topic of ‘real-world’ maths

    • For example, a carton of juice in the shape of a cuboid, a cylindrical tin and a triangular prism chocolate box all involve volume

  • Typically, the ‘real-world’ scenarios also have a cost

    • A lot of volume problems also involve calculations with money

How do I solve problems involving volume?

  • Often the 3D object in a question will not be a standard cuboid, cone, sphere, etc.

    • It will likely either be:

      • A prism (3D shape with the same cross-section running through it)

      • A portion or fraction of a standard shape (a hemisphere for example)

      • A compound object (an object made up of two or more standard 3D objects)

  • If the object is a prism, recall that the volume of a prism is the cross-sectional area × its length

    • The cross-sectional area may be a compound 2D shape

      • For example, an L-shape, or a combination of a rectangle and a triangle 

  • If the object is a fraction of a standard shape, consider the “full” version of the object and find the appropriate fraction of it

    • A hemisphere is half a sphere

    • A frustum is a truncated (chopped-off) cone or pyramid

      • The volume of a frustum will be the volume of the smaller cone or pyramid subtracted from the volume of the larger cone or pyramid

  • If the object is a compound object, find the volumes of the individual standard 3D objects and add them together

  • Problem solving questions could appear on either a non-calculator paper or a calculator paper

Examiner Tips and Tricks

  • Before you start calculating, make a quick note of your plan to tackle the question

    • For example, “Find the area of the triangle and the rectangle, add together, multiply by the length”

Worked Example

The diagram shows a prism.

L-shaped prism diagram

Work out the volume of the prism.

The volume is the area of the cross section × length (10 cm)
Find the area by splitting into a 7 × 4 and a (9 – 4) × 2 rectangle (or a 9 × 2 and a (7 – 2) × 4 rectangle)  

 7 × 4 + (9 – 4) × 2 = 38 cm2 

Find the volume (by multiplying 38 by 10)

38 × 10

380 cm3

Worked Example

The diagram shows a truncated cone (a frustum).
Using the given dimensions, find the volume of the frustum to 3 significant figures.

3-7-1-problem-solving-with-volume-2

To find the volume of the frustum, find the volume of the larger cone (30 cm tall, with a radius of 20 cm), and subtract the volume of the smaller cone (15 cm tall, with a radius of 10 cm)

Formula for the volume of a cone: 1 third pi space r squared straight h

Calculate the volume of the larger cone

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