Marlene's circular rug, radius 3 ft, cost $169. Cost per square foot?
The cost per square foot of Marlene's circular rug is $6.
To determine the cost per square foot, we first need to calculate the area of the circular rug using the formula A = πr². With a radius of 3 feet, the area computes to approximately 28.27 square feet. Dividing the total cost of $169 by the area gives a cost per square foot of about $6.
This choice represents the correct calculation of the cost per square foot. By dividing $169 by the area of the rug (approximately 28.27 square feet), we get $169 ÷ 28.27 ≈ $6, confirming this choice as accurate.
Choosing 12 suggests a miscalculation or misunderstanding of the area. If we incorrectly assumed a larger area for the rug or misapplied the division of total cost by area, we might arrive at this incorrect figure. However, the actual area calculation shows that this figure is too high for the given rug size.
This choice implies an even greater cost per square foot than option B. It could arise from an error in estimating the area or misunderstanding the formula for cost per square foot. Given the actual area, this option significantly overestimates the cost and is therefore incorrect.
Selecting 24 would indicate a severe miscalculation, suggesting an area calculation that is inconsistent with the rug's dimensions. This choice is not viable as it implies an unrealistically high cost per square foot based on the rug's actual area.
The cost per square foot for Marlene's rug is determined by accurately calculating the area and then dividing the total cost by this area. The correct answer of $6 reflects a proper understanding of these calculations, while the other options stem from various misinterpretations of the area or the cost division process. Understanding these concepts is crucial for accurate financial assessment in similar scenarios.
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