Question

What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?​

Answer 1

Solution:

$\searrow$

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. $\large\texttt{ C=\pi d }$.

Here, C is the circumference,

$\pi$ is pi, *

d is the diameter

_____________

* 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.

_____________

Alright, so now we just stick in the values.

$\boldsymbol{C=3.14\cdot30}$

$\boldsymbol{C=94.2\:inches}$

The circumference is successfully calculated.

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                                            ⚜ Area ⚜

This is the formula we will use to work out the area.

$---\mapsto\boldsymbol{A=\pi r^2}$

Here,

A denotes the area

$\pi$ denotes pi

r denotes the radius (30/2=15, because the diameter is always two times the radius)

$\large\boldsymbol{\therefore,\;the\;radius\;is\;15}$

Once again, it's just a matter of sticking in the values.

$---\mapsto\boldsymbol{A=3.14\cdot15^2}$

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.

_________________

Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.

$---\mapsto\boldsymbol{A=3.14\cdot225}$

Now, we need to multiply.

$---\mapsto\boldsymbol{A=706.5\;square\;inches}$