Question
Area \( =625 \pi \mathrm{in}^{2} \) Radius \( = \) Diameter \( = \)
Ask by Conner Floyd. in the United States
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Radius = 25 inches
Diameter = 50 inches
Solution
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
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the radius and diameter from the area of a circle, we can use the formula for the area, \( A = \pi r^2 \). Given the area \( A = 625\pi \mathrm{in}^2 \), we can set up the equation: \[ 625\pi = \pi r^2. \] By dividing both sides by \( \pi \), we get \( 625 = r^2 \). Taking the square root of both sides, we have \( r = 25 \mathrm{in} \). The diameter \( d \) is twice the radius, so \( d = 2r = 50 \mathrm{in} \). Radius \( = 25 \mathrm{in}, \) Diameter \( = 50 \mathrm{in}. \)
