WEBVTT
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The diagram shows a quarter circle which has a radius of 10 centimeters.
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Calculate the area of this quarter circle, giving your answer in terms of π.
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The area of any circle can be calculated using the formula ππ squared, multiplying the radius squared by π.
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We can therefore work out the area of a quarter circle by finding a quarter of ππ squared or ππ squared divided by four as finding a quarter is the same as dividing by four.
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The radius of our quarter circle is 10 centimeters.
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Therefore, we can calculate the area by multiplying 10 squared by π and then dividing by four.
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Squaring a number means multiplying it by itself.
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Therefore, 10 squared is equal to 10 multiplied by 10.
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This is equal to 100.
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The area is equal to π multiplied by 100 divided by four.
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π multiplied by 100 can be written as 100π.
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As we were told to give our answer in terms of π, we know there must be a π in the answer.
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Our final step is to divide 100π by four or find a quarter of 100π.
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One-quarter of 100 is equal to 25.
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We know that one-half of 100 is 50.
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Halving this again gives us 25.
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This means that 100π divided by four is equal to 25π.
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The area of the quarter circle in terms of π is 25π centimeters squared.
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Note that any time weβre calculating an area, our units are squared, centimetre squared, metre squared, et cetera.