The perimeter of a circle = 2 πr = πd

Therefore d = 36

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr².

\(\displaystyle A=\pi (5/2)^2=6.25\pi\)

1. Use the area to find the radius:

 \(\displaystyle Area=\pi r^{2}\)

\(\displaystyle 49\pi=\pi r^{2}\)

\(\displaystyle 49=r^{2}\)

\(\displaystyle r=7\)

2. Use the radius to find the diameter:

\(\displaystyle d=2r=2\cdot 7=14\)

To begin, be very careful to note that the question asks about a semi-circle—not a complete circle! This means that a complete circle composed out of two of these semi-circles would have an area of \(\displaystyle 50\pi\). Now, from this, we can use our area formula, which is:

\(\displaystyle A=\pi r^2\)

For our data, this is:

\(\displaystyle 50\pi=\pi r^2\)

Solving for \(\displaystyle r\), we get:

\(\displaystyle r=\sqrt{50}\)

This can be simplified to:

\(\displaystyle r = 5\sqrt{2}\)

The diameter is \(\displaystyle 2r\), which is \(\displaystyle 2 * 5\sqrt{2}\) or \(\displaystyle 10\sqrt{2}\).

The equation for the area of a circle is \(\displaystyle \pi r^2\), which in this case equals \(\displaystyle 39\pi\).  Therefore, \(\displaystyle r^2 = 39.\) The only thing squared that equals an integer (which is not a perfect root) is that number under a square root.  Therefore, \(\displaystyle r=\sqrt{39}\).  Since diameter is twice the radius, \(\displaystyle d=2\sqrt{39}.\)

Diameter is simply twice the radius. Therefore, \(\displaystyle 2*3=6\).

To solve, simply use the formula for the area of a circle, solve for r, and multiply by 2 to get the diameter. Thus,

\(\displaystyle A=\pi{r^2}\Rightarrow r=\sqrt{\frac{A}{\pi}}\)

\(\displaystyle r=\sqrt{\frac{4\pi}{\pi}}=\sqrt{4}=2\)

\(\displaystyle d=2r=2*2=4\)

What we are looking at is a way of dividing the pizza according to arc lengths of the crust. Thus, we need to know the total circumference first. Since the diameter is \(\displaystyle 14\), we know that the circumference is \(\displaystyle 14\pi\). Now, we want to ask how many ways we can divide up the pizza into pieces of \(\displaystyle 3\) inch crust. This is:

\(\displaystyle \frac{14\pi}{3}\) or approximately \(\displaystyle 14.66...\) pieces.

What you need to do is take this amount and subtract off \(\displaystyle 14\). This is the amount of crust that is wasted. You can then merely divide it by the original amount of divisions:

\(\displaystyle \frac{0.66076571675237...}{14.66076571675237....}=0.04507034144863....\)

(You do not need to work in exact area or length. These relative values work fine.) 

This is about \(\displaystyle 4.51\%\) of the pizza that is wasted.

To solve a question like this, first remember that the area of a circle is defined as:

\(\displaystyle A=\pi r^2\)

For your data, this is:

\(\displaystyle 45 = \pi r^2\)

To solve for \(\displaystyle r\), first divide both sides by \(\displaystyle \pi\). Then take the square root of both sides. Thus you get:

\(\displaystyle r =3.78469878303024...\)

The diameter of the circle is just double that:

 \(\displaystyle d=7.56939756606048\)

Rounding to the nearest hundredth, you get \(\displaystyle 7.57\).

The formula for the area of a circle is \(\displaystyle A=\pi r^2\), and the formula for circumference is \(\displaystyle C=2\pi r\). If we solve for C in terms of r, we get
\(\displaystyle r=C/2\pi\).

We can then substitute this value of r into the formula for the area:

\(\displaystyle A=\pi r^2\)

\(\displaystyle =\pi (C/2\pi )^2\)

\(\displaystyle =C^2\pi /4\pi ^2\)

\(\displaystyle =C^2/4\pi\)