Q:

Pizza House sells 2 different pizza sizes: A 16-inch-diameter pizza and a 12-inch-diameter pizza. How much more pizza do you get by ordering the 16 in. diameter than the smaller one

Accepted Solution

A:
The 16 inch diameter leads to a 8 inch radius (cut the diameter in half). So r = 8 is plugged into the area of a circle formula to getA = pi*r^2A = pi*8^2A = pi*64A = 64pi .... which is the exact area in terms of piWe'll use this value later, so let's call it A1 = 64piRepeat for the other pizza. We have a 12 inch diameter mean the radius is r = 6 so its area would be...A = pi*r^2A = pi*6^2A = pi*36A = 36piWe'll use this value later, so let's call it A2 = 36piNow subtract the two areas (large - small) to get the difference in areas which we'll call DD = A1 - A2D = 64pi - 36piD = (64-36)piD = 28piThe difference in the two areas is exactly 28pi square inchesNow use a calculator to find that 28*pi = 28*3.1415926535898 = 87.964594 approximately if you were to round to 6 decimal placesApproximate answer: 87.964594 square inchesnote: I went with the approximate answer because it's probably easier to visualize a fractional or decimal part of a pizza better than some number in terms of pi