Take the square root: \( r = 5 \) cm.
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- Set \( \frac{1}{3}\pi r^2 \times 12 = 100\pi \).
- Simplify: \( 4\pi r^2 = 100\pi \).
- Divide by \( 4\pi \): \( r^2 = 25 \).
- The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If \( a = 3 \), \( d = 2 \), and \( S_n = 110 \), find \( n \).
- Substitute into the formula: \( \frac{n}{2}(2 \times 3 + (n-1) \times 2) = 110 \).
- Simplify: \( \frac{n}{2}(6 + 2n - 2) = 110 \).
