Solution:
[tex]\searrow[/tex]
Detailed explanation:
Here we need to find both the circumference and the area of a circle whose diameter is 30 in.
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⚜ Circumference ⚜
This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].
Here, C is the circumference,
[tex]\pi[/tex] 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 never-ending digits 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.
[tex]\boldsymbol{C=3.14\cdot30}[/tex]
[tex]\boldsymbol{C=94.2\:inches}[/tex]
The circumference is successfully calculated.
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⚜ Area ⚜
This is the formula we will use to work out the area.
[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]
Here,
A denotes the area
[tex]\pi[/tex] denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]
Once again, it's just a matter of sticking in the values.
[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]
NB:
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.
[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]
Now, we need to multiply.
[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]
