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Area & Volume of Similar Shapes (AQA GCSE Maths)

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  • FrontSimilar Areas & Volumes

    What is the relationship between the length scale factor and the area scale factor?

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  • What is the relationship between the length scale factor and the area scale factor?

    The area scale factor, k squared, is the square of the length scale factor k.

  • What is the relationship between the length scale factor and the volume scale factor?

    The volume scale factor, k cubed, is the cube of the length scale factor k.

  • True or False?

    The cube root of the volume scale factor can be used to find an unknown length.

    True.

    The cube root of the volume scale factor is the length scale factor. This can be used to find an unknown length.

    E.g. you can find length x by finding the volume scale factor, 448 over 56 equals 8, taking its cube root, cube root of 8 equals 2, and multiplying the result by the corresponding length on object A, x equals 7 cross times 2 equals 14 space cm.

    Two similar objects. Object A has a volume of 56 cm^3 and object B has a volume of 448 cm^3. The volume scale factor is therefore 8. A length of 7 cm is marked on object A and the corresponding length on object B is labelled x.

  • How do you find the area of a similar shape from a known area using the length scale factor, k?

    E.g. how can you find Area B in the diagram below?

    Two similar objects, A and B. Object A has a front surface area of 8 cm^2 and object B has a front surface area of x cm^2. One of the edges of object A has a length of 7 cm and the corresponding length on object B has a length of 14 cm.

    To find the area of a similar shape from a known area, find the length scale factor, k, and square it to find the area scale factor, k squared. Then multiply the result by the area of the shape you know.

    E.g. to find Area B, length space scale space factor equals 14 over 7 equals 2, so area space scale space factor equals 2 squared equals 4.
    Therefore, Area space straight B equals 8 cross times 4 equals 32 space cm squared.

    Two similar objects, A and B. Object A has a front surface area of 8 cm^2 and object B has a front surface area of x cm^2. One of the edges of object A has a length of 7 cm and the corresponding length on object B has a length of 14 cm.

  • True or False?

    Multiplying the cube root of the volume scale factor by an area can be used to find a corresponding area on a similar shape.

    False.

    Multiplying the cube root of the volume scale factor by an area can not be used to find a corresponding area on a similar shape.

    The cube root of the volume scale factor, is the length scale factor. This needs to be squared to find the area scale factor, which can then be used to find a corresponding area on a similar shape.

Previous:Congruence, Similarity & Geometrical ProofNext:Pythagoras & Trigonometry

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

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      Percentages

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      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

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      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

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      Factorising

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      Completing the Square

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      Algebraic Fractions

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      Rearranging Formulas

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      Algebraic Proof

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      Linear Equations

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      Quadratic Equations

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      Simultaneous Equations

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      Iteration

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      Forming & Solving Equations

    14. Topic 14

      Functions

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      Coordinate Geometry

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      Linear Graphs

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      Graphs of Functions

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      Equation of a Circle

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      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

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      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

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      Sequences

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      Ratios

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      Problem Solving with Ratios

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      Direct & Inverse Proportion

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      Standard & Compound Units

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      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

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      Angles in Polygons & Parallel Lines

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    4. Topic 4

      Circle Theorems

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      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

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      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

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      Vectors

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      Transformations

    1. Topic 1

      Introduction to Probability

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      Simple Probability Diagrams

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      Tree Diagrams

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      Combined & Conditional Probability

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      Averages, Ranges & Data

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      Statistical Diagrams

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      Histograms

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      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation