Area $$ =625 \pi \mathrm{in}^{2} $$ Radius $$ = $$ Diameter $$ = $$

Question

UpStudy AI · Accepted Answer

To find the **radius** and **diameter** of a circle with an area of $$ 625\pi $$ square inches, you can use the following formulas:

1. **Area of a Circle:**
   $$
   A = \pi r^2
   $$
   Where:
   - $$ A $$ is the area
   - $$ r $$ is the radius

2. **Diameter of a Circle:**
   $$
   D = 2r
   $$
   Where:
   - $$ D $$ is the diameter
   - $$ r $$ is the radius

### Step-by-Step Solution

1. **Given:**
   $$
   A = 625\pi \, \text{in}^2
   $$

2. **Find the Radius ($$ r $$):**
   $$
   625\pi = \pi r^2
   $$
   Divide both sides by $$ \pi $$:
   $$
   625 = r^2
   $$
   Take the square root of both sides:
   $$
   r = \sqrt{625} = 25 \, \text{in}
   $$

3. **Find the Diameter ($$ D $$):**
   $$
   D = 2r = 2 \times 25 = 50 \, \text{in}
   $$

### **Final Answers:**
- **Radius ($$ r $$)**: $$ 25 $$ inches
- **Diameter ($$ D $$)**: $$ 50 $$ inches
Radius = 25 inches Diameter = 50 inches

Area \( =625 \pi \mathrm{in}^{2} \) Radius \( = \) Diameter \( = \)

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