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
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.
Table of Content
- What is Quadrant of a Circle?
- Area of Quadrant Formula
- How to Find the Area of Quadrant?
- Solved Examples
- Practice Problems
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