Using the Formula to Calculate the Area

Oct 13, 2025 by windailys.com 55 views

What is the Area of a Sector with a Central Angle of $$\frac{2 \pi}{9}$$ Radians and a Diameter of 20.6 mm?

In geometry, a sector is a part of a circle enclosed by two radii and an arc. The area of a sector can be calculated using the formula: Area = (θ/360) × πr^2, where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. In this article, we will explore how to calculate the area of a sector with a central angle of $$\frac{2 \pi}{9}$$ radians and a diameter of 20.6 mm.

To calculate the area of the sector, we need to first convert the central angle from radians to degrees. We are given that the central angle is $$\frac{2 \pi}{9}$$ radians. To convert this to degrees, we can use the conversion factor: 1 radian = (180/π) degrees.

import math

# Define the central angle in radians
central_angle_radians = 2 * math.pi / 9

# Convert the central angle to degrees
central_angle_degrees = (180 / math.pi) * central_angle_radians

Now that we have the central angle in degrees, we can use the formula: Area = (θ/360) × πr^2 to calculate the area of the sector. We are given that the diameter of the circle is 20.6 mm, so we can calculate the radius by dividing the diameter by 2.

# Define the diameter of the circle
diameter = 20.6

# Calculate the radius of the circle
radius = diameter / 2

Using the Formula to Calculate the Area

Now that we have the central angle in degrees and the radius of the circle, we can use the formula: Area = (θ/360) × πr^2 to calculate the area of the sector.

# Define the value of pi
pi = 3.14

# Calculate the area of the sector
area = (central_angle_degrees / 360) * pi * (radius ** 2)

Rounding the Answer to the Nearest Hundredth

Finally, we need to round the answer to the nearest hundredth. We can use the round() function in Python to do this.

# Round the answer to the nearest hundredth
rounded_area = round(area, 2)

In this article, we have explored how to calculate the area of a sector with a central angle of $$\frac{2 \pi}{9}$$ radians and a diameter of 20.6 mm. We have used the formula: Area = (θ/360) × πr^2 to calculate the area of the sector, and have rounded the answer to the nearest hundredth. The final answer is:

The final answer is: $\boxed{12.19}$
Frequently Asked Questions (FAQs) about Calculating the Area of a Sector

A: The formula for calculating the area of a sector is: Area = (θ/360) × πr^2, where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

A: To convert a central angle from radians to degrees, you can use the conversion factor: 1 radian = (180/π) degrees. For example, if the central angle is $$\frac{2 \pi}{9}$$ radians, you can convert it to degrees by multiplying it by (180/π).

A: A sector is a part of a circle enclosed by two radii and an arc. A circle is a complete shape with no beginning or end.

A: Yes, you can use the formula to calculate the area of a sector if the central angle is not in degrees. However, you will need to convert the central angle to degrees first using the conversion factor: 1 radian = (180/π) degrees.

A: Yes, you can still calculate the area of the sector if you don't know the radius of the circle. You can use the formula: Area = (θ/360) × πd^2, where d is the diameter of the circle.

A: Yes, you can use a calculator to calculate the area of a sector. Simply enter the values of the central angle, radius, and π into the calculator and press the calculate button.

A: If you make a mistake when calculating the area of a sector, you can check your answer by plugging the values back into the formula and recalculating. You can also use a calculator to check your answer.

A: The formula for calculating the area of a sector assumes that the circle is a perfect circle. If the circle is not a perfect circle, you will need to use a different formula to calculate the area of the sector.

A: The value of π in the formula is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. The value of π is approximately equal to 3.14.

A: Yes, you can use the formula to calculate the area of a sector if the central angle is greater than 360 degrees. However, you will need to use the formula: Area = (θ/360) × πr^2, where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this article, we have answered some frequently asked questions about calculating the area of a sector. We have covered topics such as the formula for calculating the area of a sector, converting central angles from radians to degrees, and using the formula to calculate the area of a sector if the circle is not a perfect circle.