A bakery charges ten cents for a cookie that is 2 inches in diameter. If the price is proportional to the area, how much do they charge for an extra large cookie that is 8 inches in diameter? Assume that each cookie is shaped of a circle.
4 times the diameter, 16 times the area
1.00
To find out how much the bakery charges for an extra large cookie with an 8-inch diameter, we first need to understand the relationship between the price and the area of the cookie.
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. Since we are given the diameter, we can calculate the radius by dividing it by 2.
For the smaller cookie:
Diameter = 2 inches
Radius = 2 inches / 2 = 1 inch
Using the area formula:
A = π(1 inch)^2
A = π square inches
For the extra large cookie:
Diameter = 8 inches
Radius = 8 inches / 2 = 4 inches
Using the area formula:
A = π(4 inches)^2
A = 16π square inches
Now, we know that the price is proportional to the area of the cookie. The ratio of the areas between the smaller and extra large cookies will be the same as the ratio of their prices.
Ratio of areas = 16π square inches / π square inches
Ratio of areas = 16
Since the ratio of areas is 16, the price of the extra large cookie will be 16 times the price of the smaller cookie.
Price of extra large cookie = 16 * 10 cents
Price of extra large cookie = 160 cents
Therefore, the bakery charges 160 cents, or $1.60, for an extra large cookie with an 8-inch diameter.