We are told the area of a circle is less than 60π square inches. Use the area formula:
A = πr²
- Set up the inequality: πr² < 60π.
- Divide both sides by π (π > 0), so r² < 60.
- Take the positive square root (radius is nonnegative): r < √60.
- Compute √60 = √(4·15) = 2√15 ≈ 7.74597, so r < 7.74597.
The largest whole-number (integer) radius less than 7.74597 is 7. Check: with r = 7 the area is π·7² = 49π < 60π, while r = 8 gives 64π > 60π, so 8 is too large.
Answer: 7 inches