Examples with solutions for Area of a Circle: Applying the formula

Exercise #1

Given that the diameter of the circle is 7 cm

What is the area?

777

Video Solution

Step-by-Step Solution

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

 πr2 \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 r=7:2=3.5

We substitute the value into the formula.

π3.52=12.25π \pi3.5^2=12.25\pi

Answer

12.25π 12.25\pi cm².

Exercise #2

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

What is its area?

333OOO

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We insert the known data:

π3²

π9

 

Answer

9π 9\pi cm²

Exercise #3

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π7²

π49

Answer

49π

Exercise #4

Look at the circle in the figure:

131313

The diameter of the circle is 13.

What is its area?

Video Solution

Step-by-Step Solution

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

S=πr2 S=\pi r^2

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

132=6.5 \frac{13}{2}=6.5

We replace in the formula and solve:

S=π×6.52 S=\pi\times6.5^2

S=42.25π S=42.25\pi

Answer

42.25π

Exercise #5

Given the semicircle:
141414
What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a circle:

S=πr2 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 r=7

We replace in the formula:S=π×72 S=\pi\times7^2

S=49π S=49\pi

Answer

24.5π

Exercise #6

A circle has a diameter of 4 cm.

What is its area?

444

Video Solution

Answer

4π 4\pi cm²

Exercise #7

The center of the circle in the diagram is O.

What is the area of the circle?

555OOO

Video Solution

Answer

25π 25\pi cm².

Exercise #8

Look at the circle in the figure:

444

The radius of the circle is 4.

What is its area?

Video Solution

Answer

16π 16π