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Toy building bricks are available in two sizes, small and large - OCR - GCSE Maths - Question 21 - 2019 - Paper 6

Question 21

Toy building bricks are available in two sizes, small and large. The small and large bricks are mathematically similar. A small brick has volume 8 cm³ and width 2.1... show full transcript

Worked Solution & Example Answer:Toy building bricks are available in two sizes, small and large - OCR - GCSE Maths - Question 21 - 2019 - Paper 6

Step 1

Calculate the length ratio using volume

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Answer

To determine the ratio of the volumes of the two bricks, we can use the formula: $\text{Ratio} = \frac{V_{large}}{V_{small}} = \frac{15.625}{8} = 1.953125$

This results in a volume ratio of approximately 1.953.

Step 2

Calculate the length ratio from volume ratio

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Answer

Since the bricks are mathematically similar, the lengths are in the cube root of the volume ratio: $\text{Length Ratio} = \sqrt[3]{1.953125} \approx 1.26$

Step 3

Calculate the width of the large brick

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Answer

Now we can find the width of the large brick. If we let ( w_{small} ) be the width of the small brick (2.1 cm), then: $w_{large} = w_{small} \times \text{Length Ratio} = 2.1 \times 1.26 \approx 2.646\, \text{cm}$

Step 4

Final calculation

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Answer

Thus, the width of a large brick is approximately 2.646 cm.

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