Solved Examples on Area of Quadrant

Example 1: A large drum is in a circular shape. Its radius is 5 units. What is the area of quadrant?

Solution:

A large drum is in circular shape means it is similar to circle, so we can use circle formulae to calculate the area of the large drum.

given, r = 5 units, π = 3.14

Area of quadrant = 1/4 × π × r²

⇒ Area of quadrant = 3.14 × 5 × 5 / 4

⇒ Area of quadrant = 19.625 units

Thus, the area of the quadrant is 19.625 units.

Example 2: If the plate is in a circular shape and its diameter is 4 units. Calculate the area of quadrant?

Solution:

We know that plate is in circular shape, and its diameter = 4 units

π = 3.14

we know that radius is half of the diameter r=d/2.

Area of quadrant = 1/4 × π ×(d/2)²

⇒ Area of quadrant = (3.14 /4) × 4 × 4 /4

⇒ Area of quadrant = 3.14 units

Therefore, the area of quadrant of the plate is = 3.14 units

Example 3: If the circumference of the circle is 8 units. Calculate its area of quadrant.

Solution:

To Calculate the area of a quadrant when the circumference of the circle is given, we need to determine the radius of the circle first using the given circumference.

The formula for the circumference of a circle is C = 2πr,

where,

• C stands for circumference
• r stands for radius

Given, the circumference is 8 units, hence 8 = 2πr

To calculate radius r:

r = 8 / (2π)

r = 1.27 units

Area of quadrant = π x (1.27 units)² / 4

⇒ Area of quadrant = 3.14 x 1.61 / 4

⇒ Area of quadrant=1.2 square units.

Therefore, the area of quadrant is 1.2 square units.

Example 4: Find the area of quadrant if the radius is 21 cm.

Solution:

given , Radius(r) = 21 cm

Now, Area of quadrant = 1/4 × π × r² cm square units

Area of quadrant = (22/7) × 21 × 21 /4

⇒ Area of quadrant = 235.93cm square units

⇒ Area of quadrant = 1386 cm²

Thus, Area of quadrant is 235.93cm square units

Example 5: Find the area of the quadrant of a circle if its radius is 14 cm.

Solution:

Given r = 14 cm, π = 22 / 7

Area of quadrant = 1/4 × π × r²

⇒ Area of quadrant = 22 / 7 × 14× 14/4

⇒ Area of quadrant = 154 cm²

Thus, the required area of quadrant = 154 cm²

Example 6: Calculate the area of quadrant by using the area of sector of a circle that subtends 60° angle at the center, and its radius is 14 cm.

Solution:

Given r = 14 cm, π = 22 / 7

Area of sector = (θ/360°) × πr²

⇒ Area of sector = (60° / 360°) × 22 / 7 × 14 x 14

⇒ Area of sector = 102.67 cm square units

⇒ Area of Quadrant = (1/4) × Area of Sector

Thus, the required area of quadrant = 25.66 cm square units

Area of a Quadrant is defined as the one-fourth space of a circle as a Quadrant is the one-fourth part of a circle. A circle is defined as the locus of a considerable number of focuses that are equidistant from the inside of the circle. When a circle is partitioned equally by drawing two perpendicular diameters, it results in making four parts of a circle. Each Part of a circle is called a Quadrant. The Areas of all four quadrants of a circle are equal, and the sum of the areas of the four quadrants is again equal to the area of the circle.

In this article, we will learn what is a Quadrant, what is an Area of Quadrant, Area of Quadrant Formula, and solve some problems based on it. So Let’s start learning about quadrants with a clear definition of the Area of Quadrant fundamental concept in mathematics.