34. Premixed concrete is sold in 80-pound bags, and each bag provides approximately 0.6 cubic feet of concrete. Which of the following is the best estimate of the number of 80-pound bags of premixed concrete needed to fill a rectangular foundation 6 feet wide by 10 feet long by 1 foot deep?
Answer: C
The best estimate of the number of 80-pound bags of premixed concrete needed is 100.
To determine the number of bags required, we first calculate the volume of the foundation, which is 6 feet wide, 10 feet long, and 1 foot deep, resulting in a total volume of 60 cubic feet. Since each 80-pound bag provides approximately 0.6 cubic feet of concrete, we divide 60 by 0.6, yielding an estimate of 100 bags.
A) 136
Option A is incorrect because it overestimates the number of bags needed. If we were to use 136 bags, that would imply a volume of approximately 81.6 cubic feet (136 bags × 0.6 cubic feet per bag), which exceeds the actual volume of the foundation (60 cubic feet).
B) 130
Option B is also incorrect as it suggests using 130 bags. This would provide around 78 cubic feet of concrete (130 bags × 0.6 cubic feet per bag), again more than the required volume of 60 cubic feet, leading to unnecessary excess concrete.
C) 100
Option C is the correct choice as it accurately estimates the number of bags needed. Dividing the total volume of the foundation (60 cubic feet) by the volume provided by each bag (0.6 cubic feet) gives exactly 100 bags, matching the requirement precisely.
D) 50
Option D is incorrect because it significantly underestimates the quantity required. Using only 50 bags would yield only 30 cubic feet of concrete (50 bags × 0.6 cubic feet per bag), which is insufficient to fill the foundation's volume of 60 cubic feet.
E) 36
Option E is incorrect as it also underestimates the need for concrete. With 36 bags, the total would be 21.6 cubic feet (36 bags × 0.6 cubic feet per bag), far less than the required 60 cubic feet for the foundation.
Conclusion
The correct answer, 100 bags, is derived from accurately calculating the volume of the foundation and the concrete volume provided by each bag. All other options fail to meet the required volume, either overestimating or underestimating the necessary amount of concrete. Thus, option C is definitively the best estimate for this scenario.