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?
Ratio: Impact of a radius change on the area of a circle
Question 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?
Question 2
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?
Question 3
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?
Examples with solutions for Ratio: Impact of a radius change on the area of a circle
Exercise #1
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
Exercise #2
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.
Exercise #3
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?