Examples of Area Calculation

Example 1: What is the area of a quarter circle in square meters if its radius is 8 meters?

Solution

If the radius of a quarter circle is 8 meters, the area of the quarter circle can be calculated using the formula: Area = (1/4) πr².

Substituting the given value, we get

Area = (1/4) x π x 8² = (1/4) x π x 64 = 16π.

Therefore, the area of the quarter circle is 16π square meters.

Example 2: In a yard, there is a flower bed that is 5-feet across and made like a quarter circle. How many square feet does this flower bed cover?

Solution:

The area of a quarter-circle shaped flower bed with a radius of 5 feet can be calculated similarly.

Using the formula Area = (1/4) πr², we get

Area = (1/4) x π x 5² = (1/4) x π x 25 = 6.25π.

Therefore, the area of the flower bed is 6.25π square feet.

Example 3: An artist is painting a picture that is 10 meters across and in the shape of a quarter circle. How big will the painting be in square meters?

Solution:

For the mural with a radius of 10 meters, the area can be found using the formula

Area = (1/4) πr².

Substituting the given value, we get

Area = (1/4) πr² = (1/4) x π x 100 = 25π.

Thus, the area of the mural is 25π square meters.

A quarter circle is one-fourth of a full circle. It resembles a slice of pie, that is divided into four equal parts. It includes a 90° angle and a curved edge, forming a right-angled sector. Calculating the area of a quarter circle is simple and useful in various applications. This article will guide you through the steps to determine the area, making it easy to understand and apply.