Video: AQA GCSE Mathematics Higher Tier Pack 2 β€’ Paper 1 β€’ Question 7

The diagram shows two quarter circles with radii 3 m. Calculate the total area of the shape. Give your answer in terms of πœ‹.

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Video Transcript

The diagram shows two quarter circles with radii three meters. Calculate the total area of the shape. Give your answer in terms of πœ‹.

To find the area of a full circle, we can use the formula πœ‹π‘Ÿ squared, where π‘Ÿ represents the radius of the circle. But we’re told that the diagram consists of two quarter circles. So to find the area of each quarter circle, we’d need to divide πœ‹π‘Ÿ squared by four. We could then multiply this by two as we have two quarter circles.

Or another way to approach this would be to think that if we put two quarter circles together, then they form a semicircle. So rather than finding the area of each quarter circle and doubling it, we could instead just find the area of a semicircle by dividing our formula πœ‹π‘Ÿ squared by two.

In this question, we’re told that the radii of the quarter circles and therefore the radius of the full circle is three meters. So substituting this value for π‘Ÿ into our formula for the area of the semicircle gives πœ‹ multiplied by three squared over two.

Three squared just means three multiplied by three which is nine and πœ‹ multiplied by nine can be written as nine πœ‹. So the area simplifies to nine πœ‹ over two. We could also write this as nine over two πœ‹ if we wish.

If we had access to a calculator, then we could evaluate what nine over two times πœ‹ is equal to as a decimal. But this question asks us to give our answer in terms of πœ‹. So we’ll leave our answer as nine over two πœ‹.

As the units for the radius were meters, the units for the area will be meters squared. So our answer is nine over two πœ‹ meters squared.

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