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Find the Area of a Circle
Problem: I need to order pizza for my department’s staff meeting. The pizza place has two deals. I can buy three medium (12") pizzas for $18 or two large (16") pizzas for $20. Which is the better deal?
Strategy: You will have to figure out the area of a 12" pizza vs. the area of a 16" pizza. The formula for the area of a circle is pi * r2 (where r is the radius). The radius of a pizza is one-half the diameter. If you enter the diameter of the pizza in B2, the radius is =B2/2.
Pi is a Greek letter that represents 3.141592654. Excel offers the PI function to return this number. It is a lot easier to remember =PI() than the many digits in 3.141592654.
Figure 372 =PI() returns the value of pi to 15-digit precision.
Here’s how you determine which is the better pizza deal:
1. Set up a worksheet. In cell B2, enter the diameter of the pizza.
2. In cell C2, calculate the radius as =B2/2.
3. In cell D2, calculate the area of the pizza in square inches, using =PI()*C2^2.
Figure 373 Area is pi times radius squared.
4. In column E, enter the quantity of pizzas.
5. Calculate the total square inches in column F by using =E2*D2.
6. Enter the cost for the special in column G. In column H, calculate the dollars per square inch of pizza, using =G2/F2.
Figure 374 Cost per square inch.
Results:From a purely mathematical point of view, the special with two large pizzas is a slightly better deal, pricing the pizza at 4.97 cents per square inch.
Additional Details: My eight-grade math teacher, Mr. Nick Irwin, would like me to mention, for the sake of completeness, that the circumference of the pizza is pi times the diameter. That would be =PI()*B2.