Circle Radius Comparison: Finding the Ratio of 16 vs 8

Question

How many times longer is the radius of the red circle than the radius of the blue circle?

168

Video Solution

Solution Steps

00:00 Find the ratio of radii between the red and blue circles
00:04 The radius of a circle equals half its diameter
00:08 This is the size of the red circle's radius
00:12 We'll use the same method to find the blue circle's radius
00:19 This is the size of the blue circle's radius
00:22 Let's substitute these values in the ratio and solve
00:31 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will calculate the ratio of the radius of the red circle to the radius of the blue circle.

Here are the steps:

  • Step 1: Identify the radii of the circles:
    Radius of the red circle is half of the diameter, rred=8 r_{\text{red}}=8
    Radius of the blue circleis half of the diameter, rblue=4 r_{\text{blue}}=4

  • Step 2: Use the formula for the ratio:
    Ratio=rredrblue=84 \text{Ratio}=\frac{r_{\text{red}}}{r_{\text{blue}}}=\frac{8}{4}

  • Step 3: Simplify the ratio:
    168=2 \frac{16}{8} = 2

Therefore, the radius of the red circle is twice the radius of the blue circle.

Therefore, the solution to the problem is 2 2 .

Answer

2 2