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The diagram shows 3 identical circles inside a rectangle - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

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The diagram shows 3 identical circles inside a rectangle. Each circle touches the other two circles and the sides of the rectangle, as shown in the diagram. The rad... show full transcript

Worked Solution & Example Answer:The diagram shows 3 identical circles inside a rectangle - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

Step 1

Work out the length of the rectangle

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Answer

Given that each circle has a radius of 24 mm, the diameter of each circle is:

Diameter=2×Radius=2×24 mm=48 mm\text{Diameter} = 2 \times \text{Radius} = 2 \times 24 \text{ mm} = 48 \text{ mm}

Since the circles are arranged in a straight line along the length of the rectangle, the length of the rectangle is:

Length=2×Diameter=2×48 mm=96 mm\text{Length} = 2 \times \text{Diameter} = 2 \times 48 \text{ mm} = 96 \text{ mm}

Step 2

Work out the height of the rectangle

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Answer

The height of the rectangle is the diameter of one circle, which is:

Height=Diameter=48 mm\text{Height} = \text{Diameter} = 48 \text{ mm}

Step 3

Calculate the area of the rectangle

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Answer

The area of the rectangle can be calculated using the formula:

Area=Length×Height\text{Area} = \text{Length} \times \text{Height}

Substituting the values:

Area=96 mm×48 mm=4608 mm2\text{Area} = 96 \text{ mm} \times 48 \text{ mm} = 4608 \text{ mm}^2

Step 4

Present the final answer

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Answer

Rounding to three significant figures, the area of the rectangle is:

[ 4600 \text{ mm}^2 ]

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