Video: AQA GCSE Mathematics Foundation Tier Pack 3 β€’ Paper 1 β€’ Question 11

The diagram shows a quarter circle which has a radius of 10 cm. Calculate the area of this quarter circle, giving your answer in terms of πœ‹.

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Video Transcript

The diagram shows a quarter circle which has a radius of 10 centimeters. Calculate the area of this quarter circle, giving your answer in terms of πœ‹.

The area of any circle can be calculated using the formula πœ‹π‘Ÿ squared, multiplying the radius squared by πœ‹. We can therefore work out the area of a quarter circle by finding a quarter of πœ‹π‘Ÿ squared or πœ‹π‘Ÿ squared divided by four as finding a quarter is the same as dividing by four. The radius of our quarter circle is 10 centimeters. Therefore, we can calculate the area by multiplying 10 squared by πœ‹ and then dividing by four.

Squaring a number means multiplying it by itself. Therefore, 10 squared is equal to 10 multiplied by 10. This is equal to 100. The area is equal to πœ‹ multiplied by 100 divided by four. πœ‹ multiplied by 100 can be written as 100πœ‹. As we were told to give our answer in terms of πœ‹, we know there must be a πœ‹ in the answer. Our final step is to divide 100πœ‹ by four or find a quarter of 100πœ‹. One-quarter of 100 is equal to 25. We know that one-half of 100 is 50. Halving this again gives us 25. This means that 100πœ‹ divided by four is equal to 25πœ‹.

The area of the quarter circle in terms of πœ‹ is 25πœ‹ centimeters squared. Note that any time we’re calculating an area, our units are squared, centimetre squared, metre squared, et cetera.

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