How do you find the area of a sector with an arc length?

Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm . Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm² . You can also use the arc length calculator to find the central angle or the circle’s radius.

How do you find the area of a sector in a circle?

Area of a Sector of Circle = (θ/360º) × πr2, where, θ is the angle subtended at the center, in degrees, and r is the radius of the circle. Area of a Sector of Circle = 1/2 × r2θ, where, θ is the angle subtended at the center, in radians, and r is the radius of the circle.

What is the relationship between the arc length and sector area of a circle?

Sector area is proportional to arc length The area enclosed by a sector is proportional to the arc length of the sector. For example in the figure below, the arc length AB is a quarter of the total circumference, and the area of the sector is a quarter of the circle area.

What is the area of the shaded sector?

Answer: The area of the shaded sector of the circle is A = (θ / 2) × r2 where θ is in radians or (θ / 360) × πr2 where θ is in degrees. Let’s see how we will use the concept of the sector of the triangle to find the area of the shaded sector of the circle.

What is the area of the 90 sector?

90∘ is 14th of 360∘, so the area of the sector is 14th the area of the circle.

What is sector formula?

To calculate the area of a sector of a circle we have to multiply the central angle by the radius squared, and divide it by 2. Area of a sector of a circle = (θ × r2 )/2 where θ is measured in radians. The formula can also be represented as Sector Area = (θ/360°) × πr2, where θ is measured in degrees.

What is the arc length of a sector?

So, for angle 360∘ the length of the circumference is 2πr. So, for angle 1∘ the length of the arc would be 2πr360. And for angle θ the length of the arc would be θ360×2πr. Hence the length of an arc of a sector of the circle would be θ360×2πr.

What are the similarities between calculating the sector area and arc length?

Both calculate fractions of the whole. Finding an arc length you find a fraction of the whole circumference of a circle. Finding the area of a sector you find a fraction of the whole area of a circle. The fraction in both cases is the item’s central angle measure divided by the angle measure of one turn.

How do you find the radius of a sector with the area and angle?

You can find the radius of both the sector and the circle by using the sector’s angle and area. Double the area of the segment. For example, if the segment area is 24 cm^2, then doubling it results in 48 cm^2.

What is the sector formula?

FAQs on Sector of a Circle Area of a sector of a circle = (θ × r2 )/2 where θ is measured in radians. The formula can also be represented as Sector Area = (θ/360°) × πr2, where θ is measured in degrees.

How to find the area of a sector of a circle?

Whenever you want to find area of a sector of a circle (a portion of the area), you will use the sector area formula: Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius. Now that you know the formulas and what they are used for, let’s work through some example problems!

How to calculate the arc length of a sector?

r = C (2π) r = C ( 2 π) Once you know the radius, you have the lengths of two of the parts of the sector. You only need to know arc length or the central angle, in degrees or radians.

Which is the formula for the arc length of a circle?

The arc length formula for polar coordinates is given by L = ∫√r2 + (dr dθ)2dθ Since r = a, then dr dθ = 0 because the derivative of a constant is always 0. Then, the formula becomes (for arc length of a circle, which is 0 ≤ θ ≤ 2π) L = ∫2π 0 √r2dθ = ∫2π 0 rdθ = rθ|θ = 2πθ = 0 = 2πr − 0 = 2πa.

How to calculate the radius of a circle?

Given the circumference, C C of a circle, the radius, r r, is: r = C (2π) r = C (2 π) Once you know the radius, you have the lengths of two of the parts of the sector. You only need to know arc length or the central angle, in degrees or radians.