To determine which stepping stone option gives the most rock for the money, we can calculate the area of both the square and round stones.
Area of the Square Stone
The area of a square is calculated using the formula: \[ \text{Area} = \text{side} \times \text{side} \] For the 12-inch by 12-inch square stone: \[ \text{Area} = 12 , \text{inches} \times 12 , \text{inches} = 144 , \text{square inches} \]
Area of the Round Stone
The area of a circle is calculated using the formula: \[ \text{Area} = \pi \times r^2 \] First, we need to determine the radius of the 13-inch round stone. The diameter is 13 inches, so the radius is: \[ r = \frac{13}{2} = 6.5 , \text{inches} \] Now we can calculate the area: \[ \text{Area} = \pi \times (6.5)^2 \approx 3.14 \times 42.25 \approx 133.57 , \text{square inches} \]
Comparison
- Area of square stone: 144 square inches
- Area of round stone: 133.57 square inches
Conclusion
Since the area of the square stepping stone (144 square inches) is greater than the area of the round stone (approximately 133.57 square inches), the square stones give you more rock for the money. Therefore, you should choose the 12" by 12" square stepping stones for the best value.
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