A pizza of diameter 16 inches has an area large enough to serve 4 people. What is the diameter of a pizza with an area large enough to serve 12 people.

Question

This is a question that I have trouble figuring out on my MATHCOUNTS packet. Could someone help me find the answer to this problem, and show me how it's supposed to be solved.

Answer 1

Lala this is a ratio problem. From what's given in the first sentence you can find out the area of a pizza for 4 people. Use the formula: Area of a circle = pi * (radius) squared. (Hint: radius is one half times diameter.) 
Once you find the area of the 1st pizza you can set up your ratio as: 1stArea/4 people = 2ndArea/12 people. In this equation you are solving for the 2nd area. I hope this makes sense so far.

Remember the problem asks for the diameter of the 2nd pizza, NOT the area. Using your area formula solve for the radius. Last, multiply the radius by two to get the diameter or the pizza able to serve 12 people.

Answer 2

A = πr²

=π8² = 201 in²

Area per person = 201/4 = 50 in²

Area needed for 12 people = 12 x 50 = 603 in²

603 = πr²

r = 13.8 in d= 2r = 28 in

Answer 3

I'm sorry. I didn't read the question carefully.

 

a = Πr²

a = Π(8)²

a = Π(64)

a ≈ 201.1 in²

201.1/4 = 50.275 in² per person

50.275 * 12 = 603.3 in² for 12 people

603.3 = Πr²

r² ≈ 603.3/Π

r² ≈ 192.0

r ≈ √192.0

r ≈ 13.86 in

d ≈ 28 in