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.
you ate 4/12 = 1/3 of the area
so you ate (1/3) pi (49)
2/3 of the circumference is left
(2/3)(pi)(14)
To find out how much of the area you have consumed, we need to determine the area of the whole pizza and the area of the four slices you have eaten.
First, let's find the area of the whole pizza. The formula for finding the area of a circle is A = πr², where A represents the area and r represents the radius. Since we know the diameter of the pizza is 14 inches, we can find the radius by dividing the diameter by 2: r = 14 inches / 2 = 7 inches.
Using the formula, we can calculate the area of the whole pizza: A = π(7 inches)² = 49π square inches.
Now, let's find the area of four slices. Since the pizza is cut into 12 equal slices, four slices would be one-third of the total number of slices: 4 slices / 12 slices = 1/3.
To find the area of one slice, we need to divide the area of the whole pizza by the number of slices: (49π square inches) / 12 slices = (49/12)π square inches.
Finally, to determine the area you have consumed, multiply the area of one slice by the number of slices you ate: (1/3) * (49/12)π square inches.
To find the length of the remaining crust, we need to consider the circumference of the pizza. The formula for the circumference of a circle is C = 2πr.
Using the radius we found earlier, the circumference of the pizza is: C = 2π(7 inches) = 14π inches.
Since you have eaten four slices, there are eight remaining slices. Assuming each slice has the same arc length, the remaining crust can be calculated by multiplying the arc length of one slice by eight.
So, to find the length of the remaining crust, we multiply the circumference of the pizza by (8/12) or 2/3: (14π inches) * (2/3) = (28/3)π inches, which is approximately 9.333π inches.
Therefore, you have consumed (1/3) * (49/12)π square inches of the area, and the remaining crust of the pizza is approximately 9.333π inches long.