Areas Related to Circles – Formula & Equation Sheet
Essential formulas and equations from Mathematic, tailored for Class 10 in Mathematics.
This one-pager compiles key formulas and equations from the Areas Related to Circles chapter of Mathematic. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Area of a circle: A = πr²
A is the area, r is the radius. This is the formula for calculating the area of a full circle.
Area of a sector: A = (πr²θ)/360
A is the area, r is the radius, θ is the angle in degrees. This determines the area of a sector based on the fraction of the full circle represented by the angle.
Length of an arc: L = (2πrθ)/360
L is the arc length, r is the radius, θ is the angle in degrees. This formula calculates the length of the arc of a sector.
Area of a segment: A = Area of sector - Area of triangle
This formula defines the area of a segment as the area of the sector minus the area of the triangle formed by the radii and the chord.
Area of major sector: A = πr² - Area of minor sector
This calculates the area of the larger remaining sector after deducting the area of the smaller sector from the total area of the circle.
Area of major segment: A = πr² - Area of minor segment
Similar to the major sector, this finds the area of the larger segment by subtracting the area of the smaller segment from the total area.
Radius from circumference: r = C/(2π)
C is the circumference; this formula allows you to find the radius when the circumference is known.
Circumference of circle: C = 2πr
C is the circumference. This formula gives the distance around the circle based on its radius.
Area of quadrant: A = (1/4)πr²
This works for circular quadrants, representing a quarter of the full circle area.
Area of a triangle using sine: A = (1/2)ab sin(θ)
A is the area, a and b are two sides, and θ is the included angle. This is used to find the area of a triangle when two sides and their included angle are known.
Equations
Angle of major sector: Major sector angle = 360° - θ
This equation helps convert the angle of the minor sector into the angle of the major sector.
Area of circle from radius: A = 3.14r²
Using π ≈ 3.14, this provides a practical approximation for area calculations.
Length of arc from angle: L = (C/360) × θ
Using C for circumference; this defines arc length based on the full circle's circumference.
Area of segment from sector: A = (πr²θ/360) - (1/2)ab sin(θ)
This gives a specific equation for calculating the area of a segment using both sector and triangle areas.
Total angle of arc in radians: θ (in radians) = θ (in degrees) × (π/180)
Converts degrees into radians, useful for certain calculations involving circles.
Total area of circle: A = 3.14 × r²
Another practical approximation for the area of a circle using π's standard value.
Radian measure of circle: θ (in radians) = L/r
This equation represents the relation between the length of an arc and its radius, giving the angle in radians.
Area in square meters: A (m²) = A (cm²)/10000
Converts area from square centimeters to square meters for larger area contexts.
Length of chord: L = 2r sin(θ/2)
This formula finds the length of the chord from the radius and the angle at the center.
Surface area of sector: A = rL/2
This expression helps find the surface area of a sector using radius and arc length.
