an apple pie is cut into 6 slices each slice is solid for 2$ the radius of the pie is 3.5 inches the central angle of the of the remaining pie is 120
4 cups of apples
To find the area of the whole apple pie, we need to calculate the area of a circle using the given radius.
The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius. Plugging in the given radius of 3.5 inches, we have:
A = π(3.5)^2
A = 3.14 * 3.5^2
A ≈ 38.465 square inches
Now, let's calculate the area of a single slice of the pie. Since the slice is solid, it will cover a fraction of the entire pie's area. To determine the fraction, we need to find the central angle's measure in radians.
We are given that the central angle of the remaining pie is 120 degrees. To convert this to radians, we can use the formula:
radians = degrees * (π / 180)
radians = 120 * (π / 180)
radians ≈ 2.094
The fraction of the pie left is equal to the central angle in radians divided by the total angle in a circle (2π radians):
Fraction of pie left = 2.094 / (2π)
Fraction of pie left ≈ 0.333 (approximately)
Since one slice covers this fraction of the pie, we can find the area of one slice by multiplying the fraction of the pie left by the total pie area:
Area of one slice = Fraction of pie left * Area of the whole apple pie
Area of one slice ≈ 0.333 * 38.465
Area of one slice ≈ 12.822 square inches
Finally, the cost of one slice is given as $2. So, if each slice has an area of 12.822 square inches, the cost per square inch would be:
Cost per square inch = Cost per slice / Area of one slice
Cost per square inch = $2 / 12.822 square inches
Cost per square inch ≈ $0.156 (approximately)
Therefore, the cost per square inch of the apple pie is approximately $0.156.