What is the area of a sector of a circle with a diameter of 10 inches?

To find the area of a sector of a circle, you need to know the angle that the sector subtends at the center of the circle in addition to the diameter or radius of the circle.

The formula for the area of a sector (A) in terms of the central angle (θ) in degrees and radius (r) is:

A = (θ / 360) * π * r^2

If you have the diameter (d), you can find the radius (r) since the radius is half of the diameter:

r = d / 2

In your case, the diameter is 10 inches, so the radius (r) would be 5 inches:

r = 10 inches / 2 r = 5 inches

However, since we don't have the central angle (θ) for the sector, we can't calculate the exact area of the sector. If you provide the central angle, you can substitute the values into the formula to get the area.

For example, if the central angle is 90 degrees, the area of the sector would be calculated as follows:

θ = 90 degrees r = 5 inches

A = (90 / 360) * π * (5^2) A = (1/4) * π * 25 A = π * (25/4) inches^2 A = (π * 25) / 4 inches^2

Once you know the central angle, just follow the formula above to find the area of the sector.

Extra: The concept of a sector in a circle is similar to a "piece of pie" or "pizza slice" within the circle. Just as you would slice a pizza into pieces, each slice is a sector of the circle.

Two important elements of a sector are the central angle and the radius. The central angle is the angle that is formed at the center of the circle by the two radii that bound the sector. The radius is the straight line from the center of the circle to any point on the circumference.

When the central angle is known, the area of the sector can be calculated as a fraction of the area of the whole circle, since the entire circle is 360 degrees. If a sector has a central angle of 90 degrees, that means it's a quarter of the circle (because 90 is a quarter of 360). Likewise, if the central angle is 180 degrees, the sector is a semicircle, or half the circle.

Understanding the area of sectors involves understanding fractions and proportions, as you're calculating what fraction of the total circle your sector represents. This is a fundamental geometric concept, which also directly applies to real-world situations like cutting cakes or any other circular objects into pieces.