How do you find the area of a sector of a circle with the radius?
The formula for sector area is simple – multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2.
What is the formula for sector of a circle?
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.
How do you find the area of a sector given the radius and arc length?
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 arcs and sectors?
Sector Area & Arc Length use different formulas:
- Sector Area = Angle Fraction x π r²
- Arc Length = Angle Fraction x π D.
How do you find area of a shaded sector 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.
What is the area of a sector?
The area of a sector is the region enclosed by the two radii of a circle and the arc. In simple words, the area of a sector is a fraction of the area of the circle.
How do you find the area of the sector of an arc?
Hence, it can be concluded that an arc of length l will subtend l/r, the angle at the centre. 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 πr 2.
What is the area of the sector with respect to length?
Area of Sector with respect to Length of the Arc. If the length of the arc of the sector is given instead of the angle of the sector, there is a different way to calculate the area of the sector. Let the length of the arc be l. For the radius of a circle equal to r units, an arc of length r units will subtend 1 radian at the centre.
How do you find the angle of the sector of a circle?
The angles subtended by the arcs PAQ and PBQ are equal to the angle of the sectors OPAQ and OPBQ respectively. When the angle of the sector is equal to 180°, there is no minor or major sector. Area of sector. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector.
How do you find the area of a circle with radius?
You can also find the area of a sector from its radius and its arc length. The formula for area, A A, of a circle with radius, r, and arc length, L L, is: A = (r × L) 2 A = (r × L) 2