Taking `pi=3.14` , find the radius and circumference of a circle whose area is :
(i) `200.96cm^(2)`
(ii) `379.94 m^(2)`

Answer

Let's solve the problem step by step.

### Part (i): Area = 200.96 cm²

1. **Write the formula for the area of a circle**:
\[ \text{Area} = \pi r^2 \]

2. **Substitute the given values**:
\[ 200.96 = 3.14 \times r^2 \]

3. **Rearrange the equation to solve for \( r^2 \)**:
\[ r^2 = \frac{200.96}{3.14} \]

4. **Calculate \( r^2 \)**:
\[ r^2 = \frac{200.96}{3.14} = 64 \]

5. **Find the radius \( r \)**:
\[ r = \sqrt{64} = 8 \text{ cm} \]

6. **Calculate the circumference**:
\[ \text{Circumference} = 2 \pi r = 2 \times 3.14 \times 8 \]

7. **Perform the multiplication**:
\[ \text{Circumference} = 2 \times 3.14 \times 8 = 50.24 \text{ cm} \]

### Summary for Part (i):
- Radius = 8 cm
- Circumference = 50.24 cm

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### Part (ii): Area = 379.94 m²

1. **Write the formula for the area of a circle**:
\[ \text{Area} = \pi r^2 \]

2. **Substitute the given values**:
\[ 379.94 = 3.14 \times r^2 \]

3. **Rearrange the equation to solve for \( r^2 \)**:
\[ r^2 = \frac{379.94}{3.14} \]

4. **Calculate \( r^2 \)**:
\[ r^2 = \frac{379.94}{3.14} = 121 \]

5. **Find the radius \( r \)**:
\[ r = \sqrt{121} = 11 \text{ m} \]

6. **Calculate the circumference**:
\[ \text{Circumference} = 2 \pi r = 2 \times 3.14 \times 11 \]

7. **Perform the multiplication**:
\[ \text{Circumference} = 2 \times 3.14 \times 11 = 69.08 \text{ m} \]

### Summary for Part (ii):
- Radius = 11 m
- Circumference = 69.08 m

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