Circle Radius Comparison: Finding the Ratio of 16 vs 8

Circle Ratios with Radius Comparisons

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

168

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

168

2

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 .

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Ratio Formula: Divide larger radius by smaller radius to compare
  • Technique: Set up 168=2 \frac{16}{8} = 2 to find how many times longer
  • Check: Verify that 16 ÷ 8 = 2, so red radius is exactly twice blue ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting radii instead of dividing
    Don't find 16 - 8 = 8 to compare circles! Subtraction tells you the difference, not how many times longer. This gives a meaningless result for ratio problems. Always divide the larger radius by the smaller radius to find the multiplicative comparison.

Practice Quiz

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Where does a point need to be so that its distance from the center of the circle is the shortest?

FAQ

Everything you need to know about this question

Why do I divide instead of subtract to compare the circles?

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When comparing sizes, division tells you how many times larger one thing is than another. Subtraction only tells you the difference. Since the question asks "how many times longer," you need to divide: 168=2 \frac{16}{8} = 2 .

What if the numbers don't divide evenly?

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That's okay! You might get answers like 2.5 times or 1.3 times. Just make sure to express your answer as a decimal or fraction, and always double-check your division.

Does it matter which circle I put on top of the fraction?

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Yes, it matters! The question asks how many times longer the red circle's radius is than the blue circle's radius. So red goes on top: redblue=168 \frac{\text{red}}{\text{blue}} = \frac{16}{8} .

How can I check if my ratio is correct?

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Multiply your answer by the smaller radius. If you get the larger radius, you're right! Check: 2×8=16 2 \times 8 = 16 ✓. This confirms the red radius is exactly 2 times the blue radius.

What if I accidentally flip the fraction?

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If you calculate 816=0.5 \frac{8}{16} = 0.5 , you're finding how many times longer the blue radius is than the red radius. Always read the question carefully to see which comparison is being asked!

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