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?
Compare Circle Areas: Finding Area Ratio of 4 cm vs 10 cm Radius Circles
Question
Video Solution
Solution Steps
00:00 How many times larger is circle 2's area than circle 1's area?
00:03 Let's use the formula for calculating circle area
00:10 Let's substitute the radius value according to the given data and solve for the area
00:17 This is circle 1's area
00:21 Let's use the same formula to calculate circle 2's area
00:29 This is circle 2's area
00:36 Let's divide the areas to find the ratio between them
00:52 Let's cancel out pi
00:57 And this is the solution to the question
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!