*Circles - challenge :)*

*Circles - challenge :)*

August 4, 2016

This is some information for a couple of the challenges we did in class today. I have provided this information for all students, but especially those who are involved in Robocup and Tournament of Minds as I know you have had a busy schedule of late!

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An example of a challenge question you might see in your test is something like this:

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This question is asking you find the radius and diameter of a circle when given the area.

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This can be a tricky question because it forces us to work backwards to find a solution. Normally we are used to being presented with the radius and diameter and having to solve the area. But not in this case.

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So how do we do it?

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Well let's start with the first question and look at the things we know.

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We know the formula for the area of a circle is:Â

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Therefore using the information provided we know:

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490.63 = 3.14 x radius x radius

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We need to try and find out the value of the radius. The only way we can do this is to isolate the radius and have it by itself.

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Our first step is to divide both sides of the equation by pi. Remember, whatever we do to one side of the equals sign we must also do to the other.

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If we divide both sides by 3.14 we are left with this:

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490.63/3.14 = radius x radius

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Therefore

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156.25cm = radius x radius

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So far so good. We have manged to get rid of pi from the equation but we are still left with two lots of radius. We really only need one.

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Our next step is find the square root of both sides of the equation. Square root is the opposite of multiplying the radius by the radius. That's why we choose this function. This will leave us with just one radius left.

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This would look like this:

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Square root of 156.25 = radius

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Therefore:

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12.5cm = radius

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Now that we know our radius it should be easy to find our diameter, as the diameter is simply double the radius.

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Therefore:

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diameter = 25cm

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Let's do the second question too.

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Again we know the formula for the area of a circle is:

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Using the information we have been provided in the question we can then say:

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219.45 = 3.14 x radius x radius

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Again we need to try and find out the value of the radius by isolating it and having it alone by itself.

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Our first step is to dive both sides by 3.14

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219.45/3.14 = radius x radius

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This becomes:

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69.88 = radius x radius

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Next, to isolate the radius by itself (after all we only want one) we take the square root of both sides. You can do this on your calculator

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square root of 69.88in = radius

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8.36in = radius

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Now we know the radius finding the diameter is simple, as the diameter is just double the radius.

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Therefore:

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diameter = 16.72in

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We could even find the circumference now if we had too.

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We know circumference = 2 x 3.14 x radius

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Therefore:

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C = 2 x 3.14 x 8.36

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C = 52.5in :)

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Have a go at answering the third question yourself. The answers will be at the bottom of this page in red. :)

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This is another example of the type of question you may see:

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These questions are asking you to find the area of a circle when provided with a circumference.Â

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Again this is a little tricky, as we are used to being provided with the radius and diameter. However just like last time, we can work backwards to solve :)

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Let's look at questions 1 and think about what we already know. The formula for circumference is:

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Therefore using the information provided we know:

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150.7 = 2 x 3.14 x radius

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We need to isolate the radius again. Once it is by itself we will know its value.

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Let's start by dividing both sides of the equation by pi. Remember, whatever we do for one side we must also do for the other.

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Therefore:

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150.7/3.14 = 2 x radius

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Therefore:

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47.99 = 2 x radius

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Next we will divide both sides by 2. This is because currently the radius i multiplied by two and the only way we can undo that is to divide it by 2. Remember, whatever we do to one side we must also do for the other.

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Therefore

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47.99/2 = radius

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Therefore:

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radius = 23.98 (or 24 if we are rounding)

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Once we know the radius we can calculate the area using the same formula as above.

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Area Â = 3.14 x 24 x 24

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Area = 1808.64 inches squared.

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Have a go at the next two questions. The answers are below :)

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Good luck guys! If you have any questions let me know!

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Mr McClorey

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ANSWERS

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Part 1 Question 3Â

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Radius = 4.19m

Diameter = 8.77m

Circumference = 26.31m

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Part 2 Question 2

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Radius = 35m

Area = 3,846.50 metres squared

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Part 2 Question 3

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Radius = 41cm

Area = 5, 278.34 centimetres squared

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