The Parts of a Circle: Calculate the ratio between radii of two circles

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, $r_{\text{red}}=8$
  Radius of the blue circleis half of the diameter, $r_{\text{blue}}=4$

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

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

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

Therefore, the solution to the problem is $2$.

To solve this problem, follow these steps:

• Step 1: Calculate the radius of the red circle.
• Step 2: Calculate the radius of the blue circle.
• Step 3: Determine the ratio of the radius of the red circle to that of the blue circle.
• Step 4: Simplify the ratio to find how many times longer the red radius is than the blue radius.

Now, let’s proceed:

Step 1: The radius of the red circle is calculated as follows:

$\text{Radius of red circle} = \frac{\text{Diameter of red circle}}{2} = \frac{24}{2} = 12$

Step 2: Similarly, the radius of the blue circle is calculated as:

$\text{Radius of blue circle} = \frac{\text{Diameter of blue circle}}{2} = \frac{12}{2} = 6$

Step 3: Determine the ratio of the red circle’s radius to the blue circle’s radius:

$\text{Ratio} = \frac{\text{Radius of red circle}}{\text{Radius of blue circle}} = \frac{12}{6}$

Step 4: Simplify this ratio:

$\frac{12}{6} = 2$

Thus, the radius of the red circle is 2 times longer than the radius of the blue circle.

To solve this problem, let's follow these steps:

• Step 1: Calculate the radius of the blue circle from its diameter.
• Step 2: Determine the ratio of the radius of the red circle to the radius of the blue circle.

Now, let's carry out each step:

Step 1: The diameter of the blue circle is 7 cm. The radius, therefore, is half of the diameter:
$\text{Radius of the blue circle} = \frac{7}{2} = 3.5 \text{ cm}$

Step 2: We now find out how many times longer the radius of the red circle (14 cm) is than the radius of the blue circle:
$\text{Ratio} = \frac{\text{Radius of the red circle}}{\text{Radius of the blue circle}} = \frac{14}{3.5} = 4$

Therefore, the radius of the red circle is 4 times longer than the radius of the blue circle.