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A circle, with centre O and radius 6 cm, contains another circle, with centre O and radius x cm - OCR - GCSE Maths - Question 21 - 2018 - Paper 2

Question 21

A circle, with centre O and radius 6 cm, contains another circle, with centre O and radius x cm. Write down an expression, in terms of π and x, for the shaded area ... show full transcript

Worked Solution & Example Answer:A circle, with centre O and radius 6 cm, contains another circle, with centre O and radius x cm - OCR - GCSE Maths - Question 21 - 2018 - Paper 2

Step 1

Write down an expression for the area of the larger circle

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Answer

The area of the larger circle with radius 6 cm is given by the formula: $A_{large} = ext{π} r^2 = ext{π} (6)^2 = 36 ext{π}$ .

Step 2

Write down an expression for the area of the smaller circle

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Answer

The area of the smaller circle with radius x cm is given by: $A_{small} = ext{π} r^2 = ext{π} (x)^2 = ext{π}x^2.$

Step 3

Calculate the shaded area

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Answer

The shaded area between the two circles is the area of the larger circle minus the area of the smaller circle: $A_{shaded} = A_{large} - A_{small} = 36 ext{π} - ext{π}x^2 = ext{π}(36 - x^2).$

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