Circle - Examples, Exercises and Solutions

We use the formula:$P=2\pi r$

We replace the data in the formula:$P=2\times8\pi$

$P=16\pi$

First we need the formula for the area of a circle:

 $\pi r^2$

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

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

$r=7:2=3.5$

We substitute the value into the formula.

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

Remember that the formula for the area of a circle is

πR²

We insert the known data:

π3²

π9

The formula for the circumference is equal to:

$2\pi r$

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

Formula of the circumference:

$P=2\pi r$

We insert the given data into the formula:

$P=2\times6\times\pi$

$P=12\pi$

To calculate, we will use the formula:

$\frac{P}{2r}=\pi$

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

$\frac{8}{4}=\pi$

$2\ne\pi$

Therefore, this situation is not possible.

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.

Area of the circle:

$S=\pi r^2$

We insert the known data:

$25=\pi r^2$

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

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

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

The radius is a straight line that extends from the center of the circle to its outer edge.

The radius is essential for calculating the circumference of the circle, which can be found using the following formula:

If we substitute in the radius we have, the formula will be:

2*π*2/3

To solve this, first we'll rearrange the formula like so:

π*2*2/3 =

We'll then multiply the fraction by the whole number:

π*(2*2)/3 =

π*4/3 =

4/3π

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:

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

$S=42.25\pi$

We begin by using the formula:

$P=2\pi r$

We then insert the given data into the formula:

$14=2\times\pi\times r$

Lastly we divide Pi by 2:

$\frac{14}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{7}{\pi}=r$

To solve the exercise, first we must remember the circumference formula:

$P= 2\pi R$

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

$31.41=2\cdot3.141\cdot R$

Keep in mind that the result can be easily simplified using Pi:

$\frac{31.41}{3.141}=2R$

$10=2R$

Finally, we simplify by 2:

$5=R$

We use the formula:

$P=2\pi r$

We insert the known data into the formula:

$50.25=3.14\times2r$

$50.25=2\times r\times3.14$

$50.25=6.28r$

$\frac{50.25}{6.28}=\frac{6.28r}{6.28}$

$r=8$

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:$S=\pi\times7^2$

$S=49\pi$