LEARN Area of a Circle Segment

You might have seen this:

Well… which is the better buy?!

We can figure this out by finding the area of the pizza slices and seeing which is a better bang for your buck.

“How do we find the area of a part of a circle” you ask?

“Read on my dear friend!”

The area of the whole pi is π(6inches)^2= 36π. To find the area of the slice, we can set up a proportion. The slice takes up 60 degrees of the whole pi (360 degrees). 60 divided by 360 then, is the ratio of the amount of pizza that is in this slice to the amount of pizza in the whole pie. if we multiply this ratio by the area of the whole pie, we get the area of our slice! (60/360)*36π=6π.

The area of the whole pi is π(7inches)^2= 49π. To find the area of the slice, we can set up a proportion. The slice takes up 45 degrees of the whole pi (360 degrees). 45 divided by 360 then, is the ratio of the amount of pizza that is in this slice to the amount of pizza in the whole pie. if we multiply this ratio by the area of the whole pie, we get the area of our slice! (45/360)*49π=6.125π.

SO the second slice IS a tad bigger than the first slice. BUT is it worth spending 20 extra cents on?

If we divide the area of each slice by its price, we get the amount of pizza we get for each dollar we spend.

6π/$1.50=4π

6.125π/$1.70=3.6π

For every dollar we spend on the first pizza slice, we get 4π squared inches of pizza.

For every dollar we spend on the second pizza slice, we get 3.6π squared inches of pizza.

We should buy the first slice!

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