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.
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
The area of the quadrant of a circle is expressed in square units.
Let us solve a problem involving the above formula.
Let us solve some problems involving the above formulas.
Area of a quadrant = (1/4)πr2
Perimeter of a quadrant = ((π/2) + 2)r
It has 90 degree angle at the center.
Example 1 :
Find the area of quadrant with radius 7 cm.
Solution :
Here r = 7 cm and π = 22/7.
= (1/4) ⋅ (22/7) ⋅ (7)2
= (1/4) ⋅ (22/7) ⋅ 7 ⋅ 7
= (1/4) ⋅ 22 ⋅ 7
= (1/2) ⋅ 11 ⋅ 7
= 11 ⋅ 3.5 = 38.5 cm2
Example 2 :
Find the area of quadrant with radius 3.5 cm.
Solution :
Here r = 3.5 cm and π = 22/7.
= (1/4) ⋅ (22/7) ⋅ (3.5)²
= (1/4) ⋅ (22/7) ⋅ 3.5 ⋅ 3.5
= (1/4) ⋅ 22 ⋅ 0.5 ⋅ 3.5
= (1/2) ⋅ 11 ⋅ 0.5 ⋅ 3.5
= 10.5 ⋅ 0.5 ⋅ 3.5
= 18.375 cm2
Example 3 :
Find the area of quadrant with radius 64 cm.
Solution :
Here r = 3.5 cm and π = 22/7.
= (1/4) x (22/7) x (64)2
= (1/4) x (22/7) x 64 x 64
= (22/7) x 16 x 64
= (22 x 16 x 64)/7
= 22528/7
= 3218.28 cm2
Example 4 :
Find the perimeter of the quadrant with radius 7 cm.
Solution :
Here r = 7 cm and π = 22/7.
Circumference of quadrant = [(Π/2) + 2]r
= [(22/14) + 2] (7)
= [(11/7) + 2] 7
= ((11 + 14)/7) 7
= 25 cm
Example 5 :
Find the perimeter of the quadrant with radius 4.2 cm.
Solution :
Here r = 4.2 cm and π = 22/7.
= [(22/14) + 2] (4.2)
= [(11/7) + 2] 4.2
= ((11 + 14)/7) 4.2
= (25/7) ⋅ 4.2
= 25(0.6)
= 15 cm
Example 6 :
Find the perimeter the quadrant with radius 14 cm.
Solution :
Here r = 14 cm and π = 22/7.
= [(22/14) + 2] (14)
= [(11/7) + 2] 14
= ((11 + 14)/7) 14
= (25/7) ⋅ 14
= 25(2)
= 50 cm
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