Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. Let’s learn what it means in a circle is.
What is Quadrant of a Circle
A quadrant of a circle is each of the quarter of a circle. It is thus a sector of 90 degrees. All four quadrants are of equal size and area. Thus, when four quadrants are joined together, it forms a circle.
Quadrant of a Circle
In the above figure, the region highlighted as ABO is one of the quadrants of the given circle and the angle AOB makes a right angle at its center.
Formulas
Area of a Quadrant of a Circle
As we know, all four quadrants have the same area. Thus calculating the area of one of the quadrants will give us the area f the other three. Also, multiplying the area of a quadrant by 4 will give us the area of the circle. Now, let us find the formula to find the area of a single quadrant.
To calculate the area of a quadrant of a circle, we should know the area of a circle. As an area of a quadrant is a quarter of the total area of the circle, we can derive the formula to calculate the quadrant of a circle as follows:
As we know, the formula to calculate the area of a circle is given as:
Area (A) = πr2, here π = 3.141 = 22/7, r = radius
Now, dividing the above formula by 4 will give the area of the quadrant of a circle,
Thus,
Area (A) of a quadrant of a circle = πr2/4
Area of Quadrant of a Circle Formula
The area of the quadrant of a circle is expressed in square units.
Let us solve a problem involving the above formula.
Find the area of a quadrant of a circle with a radius of 12 m. (Assume π = 3.141)
Solution:
As we know, Area (A) = πr2/4, here π = 3.141, r = 12 m = (3.141 × (12)2/4) m2 = 113.07 m2 Thus, the area of a quadrant of a circle with a radius of 12 m is113.07 m2
Perimeter of a Quadrant of a Circle
The perimeter of a quadrant of the circle is one-fourth of the circumference and twice the radius of the circle. It is also called the circumference of the quadrant of a circle. The formula to calculate the perimeter of a quadrant of a circle is derived below:
As we know, the formula to calculate the perimeter of a circle is given as:
Perimeter (P) = 2πr, here π = 3.141 = 22/7, r = radius
Now, dividing the above formula by 4 and adding it to twice the radius of the circle, will give the perimeter of the quadrant of a circle
Thus,
Perimeter (P) of a quadrant of a circle = 2πr/4 + 2r, which can be simplified as:
Perimeter (P) of a quadrant of a circle = πr/2 + 2r = r(π/2 + 2)
Perimeter of Quadrant of a Circle Formula
Let us solve some problems involving the above formulas.
Find the perimeter of the quadrant of a circle with a radius of 22 cm.
Solution:
As we know, Perimeter (P) = r(π/2 + 2), here π = 3.141, r = 22 cm = [22(3.141/2 + 2)] cm = [(34.55 + 44)] cm = 78.55 cm Thus, the perimeter of the quadrant of a circle with a radius of 22 cm is 78.55 cm
Find the circumference of the quadrant with a radius of 6.2 cm.
Solution:
As we know, Circumference is the other name of the perimeter of a circle. Perimeter (P) = r(π/2 + 2), here π = 3.141, r = 6.2 cm = 6.2(3.141/2 + 2) = 22.13 cm Thus, the circumference of the quadrant of a circle with a radius of 6.2 cm is 22.13 cm
The perimeter of a sheet of paper in the shape of a quadrant of a circle is 15 cm. Find its area. (Use π = 3.141).
Solution:
As we know, Perimeter (P) = r(π/2 + 2), here P = 15 cm, π = 3.141 => 15 = r(3.141/2 + 2) => 15 = r × 3.57 => r = 15/3.57 = 4.20 cm Now, as we know Area (A) = πr2/4, here π = 3.141, r = 4.20 cm = [3.141 × (4.20)2/4] = 13.85 cm2 Thus, the area of a sheet of paper in the shape of a quadrant of a circle with a perimeter of 15 cm is 13.85 cm2
