The difference between the areas of two concentric circles is `88" cm"^(2)` If the radius of the inner circle is 6 cm. then the area `("in cm"^(2))` of the larger circle is closest to: `("Take "pi=(22)/(7))`

Options

A. 196
B. 201
C. 197
D. 198

Answer

To solve the problem, we need to find the area of the larger circle given the difference in areas of two concentric circles and the radius of the inner circle.

### Step-by-Step Solution:

1. **Identify the given information:**
- The radius of the inner circle (r1) = 6 cm
- The difference in areas of the two circles = 88 cm²

2. **Write the formula for the areas of the circles:**
- Area of the inner circle (A1) = π * (r1)²
- Area of the outer circle (A2) = π * (r2)²
- The difference in areas is given by: A2 - A1 = 88 cm²

3. **Calculate the area of the inner circle:**
- A1 = π * (6)² = π * 36 cm²

4. **Set up the equation for the difference in areas:**
- A2 - A1 = 88
- π * (r2)² - π * 36 = 88

5. **Factor out π from the equation:**
- π * [(r2)² - 36] = 88

6. **Divide both sides by π (using π = 22/7):**
- [(r2)² - 36] = 88 * (7/22)
- [(r2)² - 36] = 28

7. **Solve for (r2)²:**
- (r2)² = 28 + 36
- (r2)² = 64

8. **Find r2:**
- r2 = √64
- r2 = 8 cm

9. **Calculate the area of the larger circle:**
- A2 = π * (r2)²
- A2 = π * 64
- A2 = (22/7) * 64

10. **Perform the multiplication:**
- A2 = (22 * 64) / 7
- A2 = 1408 / 7
- A2 ≈ 201.14 cm²

11. **Round to the nearest whole number:**
- The area of the larger circle is closest to 201 cm².

### Final Answer:
The area of the larger circle is approximately **201 cm²**.