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

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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 ... 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 scale factor for the volumes

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Answer

Since the bricks are mathematically similar, the ratio of the volumes of the small and large bricks can be used to find the scale factor.
Let the volume of the small brick be denoted as ( V_s = 8 \text{ cm}^3 ) and the volume of the large brick as ( V_l = 15.625 \text{ cm}^3 ).
The scale factor ( k ) is given by the cube root of the ratio of the volumes:

k=VlVs3=15.62583k = \sqrt[3]{\frac{V_l}{V_s}} = \sqrt[3]{\frac{15.625}{8}}

Step 2

Calculate the scale factor value

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Answer

Calculating the scale factor:

k=1.9531253≈1.25k = \sqrt[3]{1.953125} \approx 1.25

Step 3

Calculate the width of the large brick

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Answer

To find the width of the large brick, we use the scale factor calculated above.
If the width of the small brick is ( w_s = 2.1 \text{ cm} ), then the width of the large brick ( w_l ) can be determined by:

wl=k⋅ws=1.25⋅2.1w_l = k \cdot w_s = 1.25 \cdot 2.1
Thus,

wl=2.625 cmw_l = 2.625 \text{ cm}

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