Question

How many times greater is the area of Circle 1 than the area of Circle 2​?
Circle 1
Circle 2
8 mm
4 mm
Question content area bottom
Part 1
The area of Circle 1 is
  
enter your response here times greater than the area of Circle 2.

Answer 1

To find how many times greater the area of Circle 1 is compared to Circle 2, we first need to calculate the area of each circle using the formula for the area of a circle:

\[
\text{Area} = \pi r^2
\]

where \( r \) is the radius of the circle.

**Circle 1:**
- Radius: \( r_1 = 8 \, \text{mm} \)
- Area of Circle 1:
\[
\text{Area}_1 = \pi (8)^2 = \pi \times 64 = 64\pi \, \text{mm}^2
\]

**Circle 2:**
- Radius: \( r_2 = 4 \, \text{mm} \)
- Area of Circle 2:
\[
\text{Area}_2 = \pi (4)^2 = \pi \times 16 = 16\pi \, \text{mm}^2
\]

**Comparison of Areas:**
Now, we need to find how many times greater the area of Circle 1 is than the area of Circle 2:
\[
\text{Times greater} = \frac{\text{Area}_1}{\text{Area}_2} = \frac{64\pi}{16\pi}
\]

The \(\pi\) cancels out:
\[
\text{Times greater} = \frac{64}{16} = 4
\]

Therefore, the area of Circle 1 is **4 times greater** than the area of Circle 2.

So, the final response is:
The area of Circle 1 is **4** times greater than the area of Circle 2.