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Find in the simplest form the ratio between the circumference of a circle whose radius is 63 centimetres and the perimeter of a square whose side length is seven centimetres, where ๐ is equal to 22 over seven.
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So we have two things that we need to work out: firstly the circumference of a circle with radius 63 centimetres and secondly the perimeter of a square with side length seven centimetres.
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Letโs begin with the circle.
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The formula for finding the circumference of a circle is ๐๐ or two ๐๐, where ๐ represents the radius of the circle.
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In this question, weโre told to use 22 over seven as an approximation for ๐.
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So the circumference is two multiplied by 22 over seven multiplied by 63.
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Both seven and 63 can be divided by seven to give a simplified calculation of two multiplied by 22 multiplied by nine.
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This gives 44 multiplied by nine.
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Now recall that 44 multiplied by 10 is 440.
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So if we subtract 44 from this, weโll have the result of multiplying 44 by nine.
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Itโs 396.
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So we have the circumference of the circle.
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And next we need to work out the perimeter of a square.
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The perimeter of a square is just found by multiplying its side length ๐ by four, as all four sides are the same length.
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So in this question, the perimeter of the square is four multiplied by seven, which is 28.
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So now we know the circumference of the circle and the perimeter of the square.
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The question asked us to find in the simplest form the ratio between these two values.
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So the initial ratio between the circumference of the circle and the perimeter of the square is 396 to 28.
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Now both of these can be divided by four.
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28 divided by four is seven.
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And if we recall that four multiplied by 100 is 400, then we can see easily that 396 divided by four is 99.
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This ratio canโt be simplified any further as seven is a prime number and it isnโt a factor of 99.
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Therefore, the ratio between the circumference of the circle and the perimeter of the square in its simplest form is 99 to seven.