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.

GCSEMathsAQAHigherFlashcards4. Geometry & MeasuresArea & Volume of Similar Shapes

Area & Volume of Similar Shapes (AQA GCSE Maths)

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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, $k^{2}$ , 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, $k^{3}$ , 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, $\frac{448}{56} = 8$ , taking its cube root, $\sqrt[3]{8} = 2$ , and multiplying the result by the corresponding length on object A, $x = 7 \times 2 = 14 cm$ .
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?
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, $k^{2}$ . Then multiply the result by the area of the shape you know.
E.g. to find Area B, $length scale factor = \frac{14}{7} = 2$ , so $area scale factor = 2^{2} = 4$ .
Therefore, $Area B = 8 \times 4 = 32 {cm}^{2}$ .
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.

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