a circular pizza box logo has a sector with a central angle of 80 degrees and a diameter of 16 inches. Find the area of this sector
Why did the pizza box go to therapy? Because it couldn't handle the pressure of being a "slice" of the pie!
Now, let's calculate the area of this sector. The formula to find the area of a sector is:
Area of sector = ((Central angle / 360) * π * radius^2)
Given that the central angle is 80 degrees and the diameter is 16 inches, we can find the radius by dividing the diameter by 2:
Radius = 16 inches / 2 = 8 inches
Now we can plug in the values into the formula:
Area of sector = ((80 / 360) * π * (8)^2)
Simplifying:
Area of sector = (0.2222 * 3.1416 * 64)
Calculating:
Area of sector ≈ 44.52 square inches
So, the area of this pizza sector is approximately 44.52 square inches. Enjoy your slice of geometry!
To find the area of a sector, you can use the formula:
Area of Sector = (θ/360) * πr²
where θ is the central angle in degrees and r is the radius of the sector.
In this case, the central angle is 80 degrees and the diameter is 16 inches. Since the diameter is twice the radius, the radius is 16/2 = 8 inches.
Now we can plug in the values into the formula:
Area of Sector = (80/360) * π * 8²
= (2/9) * π * 64
≈ 14.17 square inches (rounded to two decimal places)
Therefore, the area of the sector is approximately 14.17 square inches.
To find the area of the sector, you need to know the central angle and the radius of the circle.
In this case, you are given the central angle of 80 degrees and the diameter of 16 inches. First, we need to find the radius.
The diameter of a circle is equal to twice the radius. So, in this case, the diameter is 16 inches, which means the radius is half of the diameter: 16/2 = 8 inches.
Now that we have the radius and the central angle, we can calculate the area of the sector.
The area of a sector of a circle can be found using the formula:
Area = (central angle / 360) * π * (radius)^2
Substituting in the given values, we get:
Area = (80 / 360) * π * (8)^2
Simplifying further:
Area = (2/9) * π * 64
Area = (128/9) * π
So, the area of the sector is approximately 44.96 square inches.
Round to the nearest tenth
80 degrees is 2/9 of a complete circle
so, the area is 2/9 * pi * (8/2)^2 = 32/9 pi