Suppose a slice of a 10-inch pizza has an area of 15 square inches.What is the angle of this slice?
Make a sketch to illustrate your answer.
Area of whole pizza = 100π , if by 10-inch pizza you mean a radius of 10
number of slices = 100π/15= 20.9 or 21 slices ?????
so the central angle of each slice = 360/21 = 17.1°
If the radius is 5 inches,
area = 25π
number of slices = 25π/15 = 5.2 ????
round off to 5 slices
angle at centre for each slice = 360/5.2 = 69
23°
Something tells me there is something wrong here.
Who cuts a pizza into 21 slices or 5 slices?
To find the angle of the slice, we need to determine the central angle that corresponds to a slice with an area of 15 square inches.
First, let's calculate the area of the whole pizza. We know that the pizza has a diameter of 10 inches, so the radius would be half of that, which is 5 inches. The formula to calculate the area of a circle is A = πr², where A is the area and r is the radius. Plugging in the values, we find the area of the whole pizza:
A = π(5²)
A = 25π square inches
The area of the whole pizza is 25π square inches.
Now, to find the angle, we can set up a proportion between the area of the slice and the area of the whole pizza. Since the area of the slice is 15 square inches, we can write the proportion as:
15 / (25π) = θ / 360
To solve for θ, we rearrange the proportion:
θ = (15 / (25π)) * 360
Now, let's calculate the value:
θ = (15 / (25π)) * 360
θ ≈ 82.33 degrees
Therefore, the angle of the slice is approximately 82.33 degrees.
Since it is difficult to create an illustration in text format, I recommend visualizing the pizza by drawing a circle with a diameter of 10 inches. Then, mark an angle of approximately 82.33 degrees within the circle to represent the slice.
To find the angle of the slice of pizza, we can use the formula for the area of a sector of a circle.
The formula for the area of a sector of a circle is A = (θ/360) * π * r^2, where A is the area of the sector, θ is the central angle of the sector, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, we know the area of the slice is 15 square inches and the radius of the pizza is 10 inches (since it's a 10-inch pizza).
Plugging these values into the formula, we get:
15 = (θ/360) * π * 10^2
Simplifying the equation, we get:
15 = (θ/360) * 100π
To find the value of θ, we can isolate it by dividing both sides of the equation by (100π/360):
15 / (100π/360) = θ
Simplifying further, we have:
15 * (360/100π) = θ
θ ≈ 54.19 degrees
Therefore, the angle of the pizza slice is approximately 54.19 degrees.
I apologize, but as an AI text-based bot, I cannot provide a sketch. However, I hope the explanation is helpful.