Area of Circles Examples

What is the area of a circle with radius 6?

Given the radius, we can find the area of the circle using the formula A = πr². That's all it takes.

A = πr²
A = π(6)²
A = 36π ≈ 113.1 units²

You're having a circular Jacuzzi built in your backyard. If the surface of the water will have an area of 12.57 m², what's the diameter of the Jacuzzi?

Here, we know the area but we're trying to find something else about the Jacuzzi: its diameter. We can use the area formula first and see where that gets us.

A = πr²
12.57 m² = πr²
r² ≈ 4 m²
r ≈ 2 m

So the radius of our Jacuzzi is about 2 m, but we still haven't answered the question. We're looking for diameter and luckily, d = 2r. We can easily solve for d = 2(2 m) = 4 m.

A circular garden is enclosed by a fence that's 26 feet long. What's the garden's area?

This question asks us about the area of the garden, and we'll probably find the answer in square feet (since the circumference is given in feet). We can relate circumference to radius using the equation C = 2πr.

C = 2πr
26 ft = 2πr

r ≈ 4.14 ft

Now we can use the radius of the garden to find its area.

A = πr²
A = π(4.14 ft)²
A ≈ 53.8 ft²

The garden is approximately 53.8 square feet.