Circle area - Examples, Exercises and Solutions

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

49π

Given the circle whose diameter is 7 cm

What is your area?

First, let's remember the formula for the area of a circle:

 $\pi r^2$

In the question, we are given the diameter of the circle, but we need the radius.

It is known that the radius is actually half of the diameter, therefore:

$r=7:2=3.5$

We replace in the formula

$\pi3.5^2=12.25\pi$

$12.25\pi$ cm².

O is the center of the circle in the diagram below.

What is its area?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π3²

π9

$9\pi$ cm²

Look at the circle in the figure:

The diameter of the circle is 13.

What is its area?

First, let's remember what the formula for the area of a circle is:

$S=\pi r^2$

The problem gives us the diameter, and we know that the radius is half of the diameter therefore:

$\frac{13}{2}=6.5$

We replace in the formula and solve:

$S=\pi\times6.5^2$

$S=42.25\pi$

42.25π

Look at the circle in the diagram.

AB is a chord.

Is it possible to calculate the area of the circle?

Since AB is just a chord and we know nothing else about the diameter or the radius, we cannot calculate the area of the circle.

It is not possible.

A circle has an area of 25 cm².

What is its radius?

Area of the circle:

$S=\pi r^2$

We replace the data we know:

$25=\pi r^2$

Divide by Pi:$\frac{25}{\pi}=r^2$

Extract the root:$\sqrt{\frac{25}{\pi}}=r$

$\frac{5}{\sqrt{\pi}}=r$

$\frac{5}{\sqrt{\pi}}$ cm

Given the semicircle:

What is the area?

Formula for the area of a circle:

$S=\pi r^2$

We complete the shape into a full circle and notice that 14 is the diameter.

A diameter is equal to 2 radii, so:$r=7$

We replace in the formula:$S=\pi\times7^2$

$S=49\pi$

24.5π

The following is a circle enclosed in a parallelogram:

All meeting points are tangent to the circle.
The circumference is 25.13.

What is the area of the zones marked in blue?

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

$AE=AF=3$
$BG=BF=6$

From here we can calculate:

$AB=AF+FB=3+6=9$

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

It is known that the circumference of the circle is 25.13.

Formula of the circumference:$2\pi R$
We replace and solve:

$2\pi R=25.13$
$\pi R=12.565$
$R\approx4$

The height of the parallelogram is equal to two radii, that is, 8.

And from here it is possible to calculate the area of the parallelogram:

$\text{Lado }x\text{ Altura}$$9\times8\approx72$

Now, we calculate the area of the circle according to the formula:$\pi R^2$

$\pi4^2=50.26$

Now, subtract the area of the circle from the surface of the trapezoid to get the answer:

$72-56.24\approx21.73$

$\approx21.73$

Calculate the area of a circle with a radius of 5 cm.

$25\pi$

A circle has a radius of 3 cm.

What is its area?

$9\pi$

A circle has a radius of 6 cm.

What is its area?

$36\pi$

A circle has a radius of 8 cm.

Calculate the area of the circle.

$64\pi$

A circle has a radius of 10 cm.

Calculate the area of the circle.

$100\pi$

A circle has a diameter of 14 cm.

Calculate the area of the circle.

$49\pi$

The area of the circle equals $36\pi\text{.}$

Calculate the circumference.

$12\pi$