For problems $$ 4-6 $$, find the diameter, radius, and area of a circle with the given circumference. 4. Circumference: $$ 10 \pi \mathrm{~m} $$

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UpStudy AI · Accepted Answer

To solve for the **diameter**, **radius**, and **area** of a circle given its **circumference**, we'll use the fundamental formulas related to a circle's geometry.

### Given:
- **Circumference (C)** = $$ 10\pi $$ meters

### Formulas:
1. **Circumference in terms of Diameter (d):**
   $$
   C = \pi d
   $$
2. **Circumference in terms of Radius (r):**
   $$
   C = 2\pi r
   $$
3. **Area (A) in terms of Radius:**
   $$
   A = \pi r^2
   $$

### Step-by-Step Solution:

#### 1. Finding the Diameter (d):

Using the circumference formula in terms of diameter:
$$
C = \pi d
$$
Plug in the given circumference:
$$
10\pi = \pi d
$$
Solve for $$ d $$:
$$
d = \frac{10\pi}{\pi} = 10 \text{ meters}
$$

**Diameter (d) = 10 meters**

#### 2. Finding the Radius (r):

Using the circumference formula in terms of radius:
$$
C = 2\pi r
$$
Plug in the given circumference:
$$
10\pi = 2\pi r
$$
Solve for $$ r $$:
$$
r = \frac{10\pi}{2\pi} = 5 \text{ meters}
$$

**Radius (r) = 5 meters**

#### 3. Finding the Area (A):

Using the area formula:
$$
A = \pi r^2
$$
Plug in the radius:
$$
A = \pi (5)^2 = 25\pi \text{ square meters}
$$

**Area (A) = $$ 25\pi $$ square meters**

### **Summary:**
- **Diameter:** $$ 10 $$ meters
- **Radius:** $$ 5 $$ meters
- **Area:** $$ 25\pi $$ square meters
Diameter: 10 meters Radius: 5 meters Area: $$ 25\pi $$ square meters

For problems , find the diameter, radius, and area of a circle with the given circumference.
4. Circumference:

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For problems , find the diameter, radius, and area of a circle with the given circumference. 4. Circumference: