First we calculate the area of the pizza. The area of a circle is defined as . Since our diameter is 18 inches, our radius is 18/2 = 9 inches. So the total area of the pizza is  square inches.

Since the sector of the pie he cut for himself is 36 degrees, we can set up a ratio to find how much of the pizza he cut for himself. Let x be the area of the pizza he cut for himself. Then we know, 

Solving for x, we get x=25.45 square inches, which rounds down to 25.

To find the area of a sector, we need to know the total area as well as the fractional amount of the sector at which we are looking. 

In this case, we find the total area by using the following equation:

Because line segment  is our diameter, our radius is . Thus, our total area is:

We need to go one step further to find the area of sector . Simply multiply the total area by the fractional amount that sector  covers. We are told it is  of the circle's area, so do the following:

Thus, our answer is .

To find the area of a sector, simply multiply the total area of the circle by the fraction of the part you are looking at. 

In this case, our area will come from the following:

To find the fractional part of the circle we care about, take the number of degrees in  over the total number of degrees in a circle ():

So, we find our answer by multiplying these two parts together:

The area of a sector with a certain angle will be whatever fraction of the total circle's area the angle of the sector is of . This means we divide  by , and then multiply that fraction by the total area of the circle to give us the area of the sector:

Assume Statement 1 alone. Since the circumference of the circle is not given, it cannot be determined what part of the circle  is, and therefore, the central angle of the sector cannot be determined. Also, no information about the circle can be determined. A similar argument can be given for Statement 2 being insufficient.

Now assume both statements are true. Then the length of semicircle  is equal to . The circumference is twice this, or . The radius can be calculated as , and the area, . Also,  is  of the circle, and the area of the sector can now be calculated as .

The degree measure of  is half the degree measure of the arc it intercepts, which is . We can use the measures of the two given major arcs to find , then take half of this:

Between noon and 2:40 PM, two hours and forty minutes have elapsed, or, equivalently, two and two-thirds hours. This means that the minute hand has made   revolutions.

In one revolution, the tip of an eight-foot minute hand moves  feet, or  inches.

After   revolutions, the tip of the minute hand has moved  inches.

To find arc length, we need to find the total circumference of the circle and then the fraction of the circle we are interested in. Our circumference of a circle formula is:

Where  is our radius and  is our diameter.

In this problem, our diameter is the length of , which is , so our total circumference is:

Now, to find the fraction of the circle we are interested in, we need to realize that angle  is  degrees. We know this because it is made by straight line . Armed with this knowledge, we can safely calculate the length of our arc using the following formula:

To find arc length, multiply the total circumference of a circle by the the fraction of the total circle that defines the arc with the length for which you are solving.

In this case, to find the total circumference:

To find the fraction with which we are concerned, make a fraction with the number of degrees in  in the numerator and the total degrees in a circle in the denominator:

Multiply together and simplify:

Using the formula for arc length, we can plug in the given angle and radius to calculate the length of the arc that subtends the central angle of the sector. The angle, however, must be in radians, so we make sure to convert degrees accordingly by multiplying the given angle by  :