What is the perimeter of a quadrant of a circle?

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

Kindly mail your feedback to 

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com