Need help I missed this problem on my test. My answer was 31.8in^2. The right answer was 8.0in^2
How should I have worked the problem:
A pie has a diameter of 9 inches. Each slice of the pie has a central angle of 45 degrees. What is the area of each slice of pie?
A = pi * r^2
A = 3.14 * 4.5^2
A = 3.14 * 20.25
A = 63.585 sq. in.
The pie is divided into 8 pieces.
63.585 / 8 = 7.948 sq. in. >> rounded = 8 square inches.
Find the area of a regular octagon with a perimeter of 80 inches round to the nearest tenth
To find the area of each slice of pie, you need to follow these steps:
1. Remember that the area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. But in order to use this formula, we first need to find the radius of the pie.
2. The diameter of the pie is given as 9 inches. Recall that the radius of a circle is half of its diameter, so to find the radius, divide the diameter by 2:
Radius (r) = Diameter / 2 = 9 / 2 = 4.5 inches
3. Now that you have the radius, use the formula for the area of a circle to find the area of the entire pie:
A = πr^2 = π(4.5)^2 ≈ 63.6 square inches
4. Each slice of the pie has a central angle of 45 degrees. Since there are 8 equal slices in a whole pie (360 degrees / 45 degrees per slice), each slice covers 1/8th of the total area.
5. To find the area of each slice, divide the total area of the pie by 8:
Area of each slice = Total area / Number of slices = 63.6 square inches / 8 = 7.95 square inches
So, the correct answer for the area of each slice of pie is approximately 7.95 square inches, not 31.8 square inches.
To find the area of each slice of pie, you need to first find the area of the whole pie, and then divide by the number of slices.
The area of a whole circle can be calculated using the formula: A = πr^2, where A is the area and r is the radius of the circle.
Given that the diameter of the pie is 9 inches, the radius (r) would be half of that, which is 4.5 inches.
So, the area of the whole pie is: A = π(4.5)^2 = π(20.25) = 63.585 in^2 (approximately).
Since each slice has a central angle of 45 degrees, there are 360/45 = 8 slices in total.
To find the area of each slice, you need to divide the total area of the pie by the number of slices: 63.585 in^2 / 8 = 7.98 in^2 (approximately).
Therefore, the correct answer for the area of each slice of pie is approximately 7.98 in^2, not 31.8 in^2.