1. Note: Area of a circle = pi×r²

Let's write it down as a formula, with "r" standing for the original radius:

**pi×(r+3)² - pi×r² = pi×99**

Now, let's solve it!

We can eliminate pi because it is in every term: (r+3)² - r² = 99

Expanding (r+3)²: (r+3)(r+3) - r² = 99

Becomes: r² + 2×r×3 + 3² - r² = 99

Simplifying: 2×r×3 + 3² = 99

More: 6×r + 9 = 99

More: 6×r = 90

More: r = 90/6

Finally: r = 15

Let's Check:

Original Area = pi × 15² = pi × 225

Larger Area = pi × 18² = pi × 324

Yay!!