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A circular birthday cake with a diameter of 22 centimeters is divided into 11 equal sectors.
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Using 3.14 as an approximation for ๐, find the area of one sector.
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Recall, the formula for the area of a sector with an angle of ๐ radians and a radius ๐ is one-half ๐ squared ๐.
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To be able to calculate the area of one of the sectors, weโre going to need to calculate two dimensions.
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The first is the radius.
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Remember, the radius is the length of the line that joins the centre of the circle to a point on its circumference.
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Itโs half the length of the diameter.
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Since the birthday cake has a diameter of 22 centimeters, its radius can be found by halving this value.
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Thatโs 22 divided by two, which is 11 centimeters.
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The other measure that we need to calculate is the size of the angle ๐.
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Angles around a point sum to two ๐ radians.
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And the cakeโs been split into 11 equal pieces.
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We can therefore calculate the size of ๐ by dividing two ๐ by 11.
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Thatโs two elevenths of ๐.
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All thatโs left is to substitute what we know about our sector into the formula for area of a sector.
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The area of one sector is a half multiplied by 11 squared multiplied by two-elevenths ๐.
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We can cross cancel by a factor of two and 11.
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And that tells us that the area of one of the sectors is 11๐ centimeters cubed.
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We were told however to use 3.14 as an approximation for ๐.
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So letโs substitute 3.14 into the expression for the area of a sector.
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Itโs 11 multiplied by 3.14.
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To work out 11 multiplied by 3.14, we begin by calculating 11 multiplied by 314.
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There are a number of formal written methods we could use.
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But remember, 10 multiplied by 314 is 3140.
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That means 11 multiplied by 314 is 3140 plus one more 314.
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Thatโs 3454.
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3.14 is 100 times smaller than 314.
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So our answer is going to be 100 times smaller than 3454.
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3454 divided by 100 is 34.54.
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And the area of one sector is 34.54 centimeters squared.