Zach paid $8 for a pizza with an 8-inch diameter. Aiden paid $12 for pizza with a 12-inch diameter

Question

questions are:

1. how many square inches did each get
2. find the percent of the increase in price and percent of the increase in size
3. which boy got the better deal

please help I've been working on this for a while

Answer 1

area = pi(r^2) = pi(d/2)^2 = pi(8/2)^2 = 16pi for the smaller pizza = about 16(3.14159) = about 50.27 in^2

area = pi(12/2)^2 = 36pi for the larger pizza = about 113.10 in^2

$8 for 16pi is 16pi/8 = 2pi square inches for $1

$12 for 36pi is 36pi/12 = 3pi square inches for $1

the larger pizza is the better deal, (volume discount, sort of). Aiden got the better deal, assuming diminishing marginal utility of pizza is less than diminishing marginal utility of a dollar.

the larger pizza increased in size by 36/16-1 = 9/4-1 = 5/4 = 125%

the price increased by 12/8 -1 = 3/2-1 = 1/2 = 50%

for 50% more money, you get 125% more pizza