Solution:
![\searrow](https://tex.z-dn.net/?f=%5Csearrow)
Detailed explanation:
Here we need to find <u>both</u> the circumference <u>and</u> the area of a circle whose diameter is 30 in.
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⚜ <u>Circumference </u>⚜
<u></u>
This is the formula that we use for the circumference.
.
Here, C is the circumference,
is pi, *
d is the diameter
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* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has <u>never-ending digits </u>after its decimal point.
To avoid getting never-ending numbers, we will use 3.14 for pi.
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Alright, so now we just stick in the values.
![\boldsymbol{C=3.14\cdot30}](https://tex.z-dn.net/?f=%5Cboldsymbol%7BC%3D3.14%5Ccdot30%7D)
![\boldsymbol{C=94.2\:inches}](https://tex.z-dn.net/?f=%5Cboldsymbol%7BC%3D94.2%5C%3Ainches%7D)
The circumference is successfully calculated.
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⚜ <u>Area </u>⚜
This is the formula we will use to work out the area.
![---\mapsto\boldsymbol{A=\pi r^2}](https://tex.z-dn.net/?f=---%5Cmapsto%5Cboldsymbol%7BA%3D%5Cpi%20r%5E2%7D)
Here,
A denotes the area
denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
![\large\boldsymbol{\therefore,\;the\;radius\;is\;15}](https://tex.z-dn.net/?f=%5Clarge%5Cboldsymbol%7B%5Ctherefore%2C%5C%3Bthe%5C%3Bradius%5C%3Bis%5C%3B15%7D)
Once again, it's just a matter of sticking in the values.
![---\mapsto\boldsymbol{A=3.14\cdot15^2}](https://tex.z-dn.net/?f=---%5Cmapsto%5Cboldsymbol%7BA%3D3.14%5Ccdot15%5E2%7D)
<h2>NB:</h2>
Remember the Order of Operations!
P.E.M.D.A.S.
P=Parentheses
This operation tells us to evaluate all expressions in the parentheses first, if any are present.
E=Exponents
This one tells us to evaluate all expressions with exponents, if any are present.
M=Multiplication | D=Division
Unlike the two operations above, these two are completely interchangeable.
A=Addition | S=Subtraction
Like M and D, A and S are interchangeable.
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Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.
![---\mapsto\boldsymbol{A=3.14\cdot225}](https://tex.z-dn.net/?f=---%5Cmapsto%5Cboldsymbol%7BA%3D3.14%5Ccdot225%7D)
Now, we need to multiply.
![---\mapsto\boldsymbol{A=706.5\;square\;inches}](https://tex.z-dn.net/?f=---%5Cmapsto%5Cboldsymbol%7BA%3D706.5%5C%3Bsquare%5C%3Binches%7D)