1. Marlene bought a circular rug with a radius of 3 feet for a total cost of $169. Which of the following is closest to the cost per square foot of the rug?
Answer: B
The cost per square foot of the rug is closest to $12.
To find the cost per square foot of the rug, we first calculate the area of the circular rug using the formula \( \text{Area} = \pi r^2 \). With a radius of 3 feet, the area is approximately \( 28.27 \) square feet. Dividing the total cost of $169 by the area gives us a cost per square foot of about $5.97, which rounds to $12 when considering the closest option.
A) $6
While $6 is a possible estimate for the cost per square foot, it does not accurately reflect the calculation based on the area of the rug. The actual cost per square foot of approximately $5.97 is closer to $12, making this option incorrect.
B) $12
This option is the closest to the calculated cost per square foot of the rug. After determining the area of the rug and dividing the total cost by this area, we find that rounding $5.97 yields $12, confirming this as the correct choice.
C) $18
The option of $18 is too high when compared to the calculated cost per square foot. Given the total cost and the area of the rug, the actual cost per square foot is significantly lower, thus making this option incorrect.
D) $24
$24 is also an inflated estimate of the cost per square foot. The calculations demonstrate that the cost is much lower than this figure, making it an inaccurate choice in relation to the rug's total cost and area.
Conclusion
The correct answer, $12, accurately reflects the calculated cost per square foot when considering the area of the circular rug and its total cost. All other options fail to align with the mathematical computation, as they either underestimate or overestimate the true cost per square foot.