Sample Test Paper for Class 10- Areas Related to Circle
What is Area Related to Circles
The area of a circle is the amount of space it occupies in two-dimensional space. It is calculated using the formula: A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14 and r is the radius of the circle. The area of a circle can also be found using the diameter of the circle, using the formula: A = (π/4)d^2, where d is the diameter of the circle
Area of sector
A sector of a circle is a portion of the circle enclosed by two radii and an arc. The area of a sector can be calculated using the formula: A = (θ/360)πr^2, where A is the area of the sector, θ is the measure of the central angle in degrees, and r is the radius of the circle.
Alternatively, you can use the formula A = (n/360)πd^2 where n is the measure of the central angle in degrees, d is the diameter of the circle
How to find area of minor sector
A minor sector of a circle is a portion of the circle enclosed by two radii and an arc that is less than half of the full circle. To find the area of a minor sector, you can use the same formula as for a sector: A = (θ/360)πr^2, where A is the area of the minor sector, θ is the measure of the central angle in degrees, and r is the radius of the circle.
Alternatively, you can use the formula A = (n/360)πd^2 where n is the measure of the central angle in degrees and d is the diameter of the circle.
It is important to note that the measure of the central angle, θ or n must be less than 180 degrees for the sector to be considered a minor sector.
How we find area of major sector
A major sector of a circle is a portion of the circle enclosed by two radii and an arc that is greater than half of the full circle. To find the area of a major sector, you can use the same formula as for a sector: A = (θ/360)πr^2, where A is the area of the major sector, θ is the measure of the central angle in degrees, and r is the radius of the circle.
Alternatively, you can use the formula A = (n/360)πd^2 where n is the measure of the central angle in degrees, d is the diameter of the circle.
It is important to note that the measure of the central angle, θ or n must be greater than 180 degrees for the sector to be considered a major sector.
You can also find the area of a major sector by subtracting the area of the minor sector from the area of the full circle. The area of the full circle is πr^2 and the area of the minor sector can be calculated using the formula A = (θ/360)πr^2, where θ is less than 180 degrees.
Area of major sector = πr^2 - Area of minor sector.
Thu Jan 12, 2023
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