The formula for sector area is simple – multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2.
How do you find the area of a sector step by step?
To calculate the area of a sector, start by finding the central angle of the sector and dividing it by 360. Next, take the radius, or length of one of the lines, square it, and multiply it by 3.14. Then, multiply the two numbers to get the area of the sector.
How do you find the area of a sector with an arc length?
Let’s say it is equal to 45 degrees, or π/4. 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.
What is sector area?
Area of Sector. The area of a sector of a circle is the amount of space enclosed within the boundary of the sector. A sector always originates from the center of the circle. The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them.
How do you find the area of a sector of a circle without angle?
Thus the equation of circle is x²+y²=r². The equation of the chord at ‘a’ distance from center is ax-ry- ar=0 or Y= a/r(x-r). the area of sector can be found by relating it to area of segment where the area of segment is found without the usage of angle made by the chord.
What is the area of an arc?
So, if l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the centre, then; θ = l/r, where θ is in radians. When the angle of the sector is 2π, then the area of the sector (whole sector) is πr2.
How do you find the area of the shaded region of a circle?
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 formula of area of segment?
The area of the segment of the circle (or) minor segment of a circle is: (θ / 360°) × πr2 – (1/2) r2 sin θ (OR) r2 [πθ/360° – sin θ/2], if ‘θ’ is in degrees. (1/2) × r2θ – (1/2) r2 sin θ (OR) (r2 / 2) [θ – sin θ], if ‘θ’ is in radians.
What is the formula for an arc of a circle?
The formula to measure the length of the arc is – Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°) Arc Length Formula (if θ is in radians) s = ϴ × r.
What is a sector in circle?
A circular sector, also known as circle sector or disk sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.
What is an example of a sector?
To recall, a sector is a portion of a circle enclosed between its two radii and the arc adjoining them. For example, a pizza slice is an example of a sector representing a fraction of the pizza.
