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?

Rationale

Approximately 100 bags of premixed concrete are needed to fill the foundation.

To determine the number of 80-pound bags required, we first calculate the volume of the foundation. The volume is given by the formula for the volume of a rectangular prism: length × width × depth, which in this case is 10 feet × 6 feet × 1 foot = 60 cubic feet. Given that each bag provides about 0.6 cubic feet, we divide the total volume by the volume per bag: 60 cubic feet ÷ 0.6 cubic feet/bag = 100 bags.

A (136) YOUR ANSWER

Choosing 136 bags would imply an estimate that suggests a much larger volume than is necessary for the given foundation dimensions. This option overestimates the amount of concrete needed by approximately 36 bags, which is not justified given the calculated volume of 60 cubic feet.

B (130) YOUR ANSWER

This estimate of 130 bags is also too high, suggesting a volume requirement of about 78 cubic feet. This is still greater than the foundation's actual volume of 60 cubic feet, leading to an unnecessary excess of concrete that does not align with the dimensions provided.

C (100) CORRECT

This choice accurately reflects the calculation based on the foundation's volume and the amount of concrete each bag provides. With a total volume of 60 cubic feet and bags yielding 0.6 cubic feet each, needing approximately 100 bags is the correct estimation.

D (50) YOUR ANSWER

Selecting 50 bags would drastically underestimate the volume needed, suggesting only 30 cubic feet of concrete. Since the foundation requires 60 cubic feet, this choice would result in insufficient concrete to fill the foundation.

E (36) YOUR ANSWER

This option also underestimates the requirement, yielding only 21.6 cubic feet of concrete. Given the foundation's 60 cubic feet volume, this amount is far too low, leading to a significant shortfall.

Conclusion

In estimating the number of premixed concrete bags required for a rectangular foundation, accurate calculations reveal that approximately 100 bags are necessary based on the foundation's dimensions of 6 feet wide, 10 feet long, and 1 foot deep. Other choices either overestimate or underestimate the concrete needed, making them unsuitable for this scenario.

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?

Approximately 100 bags of premixed concrete are needed to fill the foundation.

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