Answer:
Therefore:
a) The area of your slice is 32/3π square inches (exact answer).
b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).
Explanation:
a) To find the area of 1/6 of the pizza, we need to determine the area of the entire pizza and then divide it by 6.
The diameter of the pizza (including the cheesy crust) is 16 inches, which means the radius is half of the diameter, so the radius is 16/2 = 8 inches.
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Therefore, the area of the entire pizza is A = π(8 inches)² = 64π square inches.
To find the area of 1/6 of the pizza, we divide the area of the entire pizza by 6:
Area of 1/6 of the pizza = (64π square inches) / 6
b) The cheesy crust is located on the outer edge of the pizza, forming the circumference of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference and r is the radius.
The length of the outside cheesy crust that belongs to your friend is 1/6 of the circumference. So, we divide the circumference by 6:
Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6
To get the exact answers, we leave the values in terms of π:
a) Area of 1/6 of the pizza = (64π square inches) / 6 = 32/3π square inches (exact answer)
b) Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6 = 16/3π inches (exact answer)
Therefore:
a) The area of your slice is 32/3π square inches (exact answer).
b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).