Question

A bakery charges $0.30 for a cookie that is 3 inches in diameter. If the price is proportional to the area, how much do they charge for an extra large cookie that is 6 inches in diameter? Assume that each cookie is shaped of a circle.

a]$0.60
b]$1.20
c]$1.80
d]$2.40

Answer 1

b.

Answer 2

if you multiply the diameter by 2, you multiply the area by \[2^{2}\]. So you multiply it by 4. So the price will be multiplied by 4 also.

Answer 3

Remember radius r is half the diameter.

Area of 3 inch cookie = \[(\pi)(r ^{2})\] = \[(\pi)(1.5 ^{2})\] = 2.25\[\pi\]

Area of 6 inch cookie = \[(\pi)(r ^{2})\] = \[(\pi)(3 ^{2})\] = 9\[\pi\]

which is 4 times bigger.

Remember, you need four 3 inch cookies to have the same amount (area!) of cookie as you get in one 6 inch cookie.

Same goes for pizza - so watch out for those special offers ;-)