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The diagram shows a cube - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 3

Question 18

The diagram shows a cube. AH = 11.3 cm correct to the nearest mm. Calculate the lower bound for the length of an edge of the cube. You must show all your working. ... show full transcript

Worked Solution & Example Answer:The diagram shows a cube - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 3

Step 1

Calculate the lower bound of AH

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Answer

Since AH is given as 11.3 cm correct to the nearest millimeter, we first need to determine the lower bound for this measurement.

To find the lower bound for a measurement that is rounded to the nearest millimeter, we subtract half of the rounding value from the given measurement:

The rounding value is 1 mm.
Half of this is 0.5 mm.

Thus, the lower bound of AH is:

$ext{Lower Bound} = 11.3 ext{ cm} - 0.05 ext{ cm} = 11.25 ext{ cm}$

Step 2

Find the length of an edge of the cube

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Answer

In a cube, the length of the edge (let's denote it as 's') can be related to the length of the diagonal (AH in this case) using the formula for the diagonal of a cube:

$d = s \sqrt{3}$

Where 'd' is the diagonal.

Rearranging the formula to find 's':

$s = \frac{d}{\sqrt{3}}$

Using the lower bound:

$s = \frac{11.25 ext{ cm}}{\sqrt{3}} \approx 6.5 ext{ cm}$

Therefore, the lower bound of the length of an edge of the cube is approximately 6.5 cm.

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