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The diagram shows a circle inside a square of side 12 cm - OCR - GCSE Maths - Question 27 - 2023 - Paper 1

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Question 27

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The diagram shows a circle inside a square of side 12 cm. Work out the percentage of the square that is shaded. You must show your working.

Worked Solution & Example Answer:The diagram shows a circle inside a square of side 12 cm - OCR - GCSE Maths - Question 27 - 2023 - Paper 1

Step 1

Step 1: Calculate the Area of the Square

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Answer

The area of a square is given by the formula:

extArea=extside2 ext{Area} = ext{side}^2

For a square with a side length of 12 cm:

extArea=122=144extcm2 ext{Area} = 12^2 = 144 ext{ cm}^2

Step 2

Step 2: Calculate the Area of the Circle

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Answer

The radius of the circle is half the side of the square:

ext{Radius} = rac{12}{2} = 6 ext{ cm}

The area of a circle is given by the formula:

ext{Area} = rac{22}{7} r^2

Substituting the radius:

ext{Area} = rac{22}{7} imes 6^2 = rac{22}{7} imes 36 = rac{792}{7} ext{ cm}^2 \\ ext{(approximately 113.14 cm}^2\text{)}

Step 3

Step 3: Calculate the Shaded Area

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Answer

The shaded area is the area of the square minus the area of the circle:

extShadedArea=extAreaofSquare−extAreaofCircle ext{Shaded Area} = ext{Area of Square} - ext{Area of Circle}

Step 4

Step 4: Calculate the Percentage of the Shaded Area

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Answer

The percentage of the square that is shaded is calculated by:

ext{Percentage} = rac{ ext{Shaded Area}}{ ext{Area of Square}} imes 100 ext{%}

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