You order a pizza. The pizza has a diameter of 14 inches and it is cut into 12 equal slices. You eat four slices, how much of the area have you consumed. How long is the remaining crust.
Area = πr^2
d = 2r
Circumference = πd
For consumed, 4/12.
For crust, 8/12 remain.
YO mo.
A circular pizza is cut into 8 slices. If the radius of the pizza is 15 ft and each central angle is 45 degrees , find the length of one piece of crust. Leave answer in terms of pi.
To find out how much of the area you have consumed, you need to calculate the area of the whole pizza and then subtract the area of the four slices you have eaten.
To calculate the area of a circle, you need to use the formula A = πr^2, where A represents the area and r represents the radius. Since you are given the diameter of the pizza, which is 14 inches, you can find the radius by dividing the diameter by 2.
Radius (r) = Diameter ÷ 2 = 14 ÷ 2 = 7 inches
Now you can calculate the area of the whole pizza using the formula:
A = πr^2 = π × 7^2 ≈ 154 square inches
Since the pizza is cut into 12 equal slices, each slice will have an equal portion of the total area. To find the area of one slice, you can divide the total area of the pizza by the number of slices:
Area of one slice = Total area ÷ Number of slices = 154 ÷ 12 ≈ 12.83 square inches
Since you have eaten four slices, you can calculate the total area you have consumed by multiplying the area of one slice by the number of slices you have eaten:
Total area consumed = Area of one slice × Number of slices eaten = 12.83 × 4 = 51.32 square inches
Therefore, you have consumed approximately 51.32 square inches of pizza.
To find out the length of the remaining crust, you need to calculate the circumference of the pizza and then subtract the circumference of the four slices you have eaten. The formula to calculate the circumference of a circle is C = 2πr.
Circumference of the pizza = 2πr = 2π × 7 ≈ 44 inches
Since each slice has a curved crust, you can estimate that each slice has approximately the same amount of crust. So to find the length of the remaining crust, subtract the circumference of the four slices you have eaten from the total circumference of the pizza:
Remaining crust length = Total crust length - 4 × Circumference of one slice
= 44 - (4 × Circumference of one slice)
To calculate the circumference of one slice, divide the circumference of the pizza by 12 and then multiply by the number of slices you have eaten:
Circumference of one slice = Circumference of the pizza ÷ Number of slices = 44 ÷ 12 ≈ 3.67 inches
Remaining crust length = 44 - (4 × 3.67) ≈ 44 - 14.68 ≈ 29.32 inches
Therefore, the remaining crust length is approximately 29.32 inches.