How to find the area of a circle using its diameter

This post is to explain how to find the area of a circle when its diameter is given, instead its radius. There are two main methods to do this task.

When it comes to find the area of a circle, there are couple of techniques and formulas used for the purpose. In previous post you have found the information on how to find the area of a circle using its radius in the formula. This post is all about finding the circle area, when we are given with its diameter.

As you know that diameter is the chord of the circle which passes through its center and its the longest chord of the circle too. There are two ways to find the area of circle when its diameter is given. Both methods are explained one by one, on this page.

1. Using diameter in the formula for area of a circle:

When the diameter of the circle is given and students want to use it in the formula, then there is the following formula to find the area of the circle using its diameter;

Consider the letter “d” represents the diameter of the circle, then the area “A” of the circle can be obtained by using the following formula:

Remember Pi (p) is a constant whose value is 3.14. Consider the diameter of the circle d = 2 cm, then we can calculate its area as shown below:

Area A = 3.14 x 2 x 2 ÷ 4

A = 3.14 x 4 ÷ 4

A = 3.14 sq.cm

2. Using Radius in the formula to find area:

Some kids just don’t like to memorize many formulas for the same task. Also, we suggest using only one formula to find the area, which makes the use of the radius of the circle.

As we know that radius times 2 is diameter, hence we can calculate radius from diameter by dividing it by 2. Consider the same above example, but first find the radius from the diameter by dividing it by 2.

Diameter of the circle “d” = 2 cm

Hence, its radius “r” = d ÷ 2 = 2 ÷ 2 = 1 cm

Now find the area of the circle using the formula with radius as shown below;

Area A = pi x radius x radius

A = 3.14 x 1 x 1

A = 3.14 x 1 = 3.14 sq.cm

Notice that the calculated area of the circle is same in both the methods. We suggest to use the same formula to find the area of a circle which uses radius in it.

Kids can do the following problems to find the circle area, when its diameter is given.

1. Find the area of a circular field whose diameter is 12 yards.

2. What is the area of a clock which have a diameter of 25 cms.

3. The diameter of a dinner plate is 10 inches, find its area.

4. A circle have a diameter of 4 inches, find its area.

5. A circular garden have a diameter of 120 yards. The cost to grass the garden is $2.5 per square yard. Find the total cost to plant the grass in whole garden.

Use the following worksheet to practice finding area of a circle using its diameter:

Finding The Area Of A Circle Using Its Diameter

Any one of the above methods can be used to find the areas of circles in each problem.

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