Ratio: Impact of a radius change on the area of a circle

Examples with solutions for Ratio: Impact of a radius change on the area of a circle

Exercise #1

There are two circles.

One circle has a radius of 4 cm, while the other circle has a radius of 10 cm.

How many times greater is the area of the second circle than the area of the first circle?

Video Solution

Step-by-Step Solution

The area of a circle is calculated using the following formula:

where r represents the radius.

Using the formula, we calculate the areas of the circles:

Circle 1:

π*4² =

π16

Circle 2:

π*10² =

π100

To calculate how much larger one circle is than the other (in other words - what is the ratio between them)

All we need to do is divide one area by the other.

100/16 =

6.25

Therefore the answer is 6 and a quarter!

Answer

$6\frac{1}{4}$

Exercise #2

There are two circles.

The length of the diameter of circle 1 is 4 cm.

The length of the diameter of circle 2 is 10 cm.

How many times larger is the area of circle 2 than the area of circle 1?

Video Solution

Answer

$6\frac{1}{4}$

Exercise #3

There are two circles.

The length of the radius of circle 1 is 6 cm.

The length of the diameter of circle 2 is 12 cm.

How many times greater is the area of circle 2 than the area of circle 1?

Video Solution

Answer

They are equal.