One can of pumpkin pie mix will make a pie of diameter 8 in. If two cans of pie mix are used to make a larger pie of the same thickness, find the diameter of that pie. Use sqrt 2 is equal to about 1.414
Duplicate post; already answered
11.312
To find the diameter of the larger pie, we can use the concept of the ratio of areas.
First, let's calculate the area of the original pie using the formula for the area of a circle:
Area = π * (radius^2)
Given that the diameter of the original pie is 8 inches, we can calculate the radius as half of the diameter:
Radius = 8 inches / 2 = 4 inches
Substituting this value into the formula, we have:
Area = π * (4 inches)^2 = 16π square inches
Now, let's consider the larger pie made with two cans of pie mix. Since the thickness remains the same, the volume of the mixture used to make the larger pie is doubled. This means that the ratio of the areas of the larger and original pie will be equal to 2.
Let's represent the diameter of the larger pie as 'x' inches. The radius will then be 'x/2'.
Using the ratio of areas, we can set up the following equation:
(π * (x/2)^2) / (16π) = 2
Simplifying the equation:
(x/2)^2 = 2 * 16
(x/2)^2 = 32
Taking the square root of both sides, we use the given approximation √2 ≈ 1.414:
x/2 ≈ √32 ≈ √(16 * 2) ≈ 4 * √2 ≈ 4 * 1.414 ≈ 5.656
Now, solve for 'x':
x ≈ 2 * (5.656) ≈ 11.312
Therefore, the diameter of the larger pie made with two cans of pie mix is approximately 11.312 inches.