Bob orders a medium pepperoni pizza that is cut into 8 slices. The radius of Bob’s pizza is 6 inches. What is the central angle of ONE slice?
360/8 = ?
To find the central angle of one slice of the pizza, we need to use the formula for the area of a sector.
The formula for the area of a sector is A = (θ/360) * π * r^2, where A is the area, θ is the central angle in degrees, r is the radius, and π is a constant approximately equal to 3.14159.
In this case, we know the radius is 6 inches and the number of slices is 8.
1. First, let's find the area of the whole pizza:
A = (360/360) * π * 6^2
A = π * 36
A = 36π square inches
2. Now, let's find the area of one slice:
Each slice is 1/8th of the whole pizza, so the area of one slice is:
(1/8) * 36π
36π/8
4.5π square inches
To find the central angle of one slice, we can equate the area of one slice to the formula for the area of a sector and solve for θ:
4.5π = (θ/360) * π * 6^2
We can simplify this equation further:
4.5π = (θ/360) * 36π
Dividing both sides of the equation by 36π:
4.5/36 = θ/360
0.125 = θ/360
Now, we can solve for θ by multiplying both sides of the equation by 360:
0.125 * 360 = θ
45 = θ
So, the central angle of one slice of Bob's pizza is 45 degrees.
To calculate the central angle of one slice, we need to use the formula for the central angle of a circle.
The formula is: Central angle = (Arc length / Radius) * 360 degrees
In this case, since the pizza is cut into 8 slices, we can assume that the arc length of one slice is equal to the circumference of the pizza divided by 8.
The formula for the circumference of a circle is: Circumference = 2 * π * Radius
Plugging in the given radius of 6 inches, we can calculate the circumference as follows:
Circumference = 2 * π * 6
Circumference = 12π inches
Now, we can find the arc length of one slice by dividing the circumference by 8:
Arc length = (12π inches) / 8
Arc length = (3π/2) inches
Finally, we can calculate the central angle of one slice by using the formula:
Central angle = (Arc length / Radius) * 360 degrees
Plugging in the values:
Central angle = [(3π/2 inches) / 6 inches] * 360 degrees
Central angle = (0.25π) * 360 degrees
Using an approximation for π (3.14), we have:
Central angle ≈ (0.25 * 3.14) * 360 degrees
Central angle ≈ 0.785 * 360 degrees
Central angle ≈ 282.6 degrees
Therefore, the central angle of one slice of the medium pepperoni pizza is approximately 282.6 degrees.