# How to Find the Area of a Quarter Circle?

When a circle is divided into $$4$$ equal parts, $$4$$ quadrants are formed, and each of these quarters is known as a quadrant. In this guide, you will learn more about the quarter circle and how to find its area. A quarter-circle is one-fourth part of the whole circle. So, the area of a quarter circle is the fourth part of the whole area of a circle.

## Step by step guide tofinding the area of a quarter circle

A circle is a collection of points that are at a constant distance from a fixed point. This fixed point and fixed distance are called “center” and “radius”, respectively. A quarter-circle is one-fourth. So the area of a quarter circle is exactly one-fourth of the area of a full circle.

### Area of a quarter circle using radius

We know that the area of a circle is $$πr^2$$. A quarter-circle is one-fourth portion of a full circle, so its area is one-fourth of the area of the circle. Thusthe area of a quarter circle in terms of radius $$\color{blue}{= \frac{πr^2}{4}}$$

### Area of a quarter circle using the diameter

Since we have $$d = 2r$$, $$r= \frac{d}{2}$$. By substituting it in the above formula, we can get the area of a quarter circle in diameter.

The area of a quarter circle $$\color{blue}{= \frac{π(\frac{d}{2})^2}{ 4 }= \frac{πd^2}{16}}$$

### How to find the area of a quarter circle?

Here are the steps to find the area of a quarter circle:

• If the radius $$(r)$$ is given, immediately replace it with the formula $$\frac{πr^2}{4}$$.
• If the diameter $$(d)$$ is given, solve $$d = 2r$$ for $$r$$ and use the formula $$\frac{πr^2}{4}$$ (or) immediately replace the value of d in the formula $$\frac{πd^2}{16}$$.
• When the circumference $$(C)$$ is given, solve $$C = 2πr$$ for $$r$$ and replace it in the formula $$\frac{πr^2}{4}$$.
• When area $$(A)$$ is given, solve $$A = πr^2$$ for $$r$$ and replace it with the formula $$\frac{πr^2}{4}$$ (or) simply find $$\frac{A}{4}$$.

### Finding Area of a Quarter Circle– Example 1:

A circle has a diameter of $$32\space cm$$, find the area of a quarter circle. $$(\pi =3.14)$$

Solution:

Diameter of circle $$= 32\space cm$$

Area of a quarter circle $$= \frac{πd^2}{16}$$

$$=\frac{3.14 × 32^2}{16}$$

$$=\frac{3.14 × 32×32}{16}$$

$$=\frac{3215.36}{16}$$

$$=200.96\space cm^2$$

## Exercises forFinding Area of a Quarter Circle

1. Find the area of the quadrant with a radius $$24\space cm$$.
2. Find the area of the quadrant with a diameter $$16 \space in$$
1. $$\color{blue}{452.16\space cm^2}$$
2. $$\color{blue}{50.24 \space in^2}$$

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