Violet has a flower box that has a rectangular base of 5 ft by 3 ft and a height of 2 ft. She wants to fill the flower box with potting soil. Potting soil is sold in bags that each contain 0.75 cubic feet of soil. How many bags of potting soil are needed to fill the flower box?
Violet needs 40 bags of potting soil to fill the flower box.
To determine the number of bags needed, first calculate the volume of the flower box by multiplying its dimensions: 5 ft × 3 ft × 2 ft = 30 cubic feet. Since each bag contains 0.75 cubic feet of soil, divide the total volume by the volume per bag: 30 ÷ 0.75 = 40 bags.
Choosing 24 bags suggests a total volume of 18 cubic feet (24 × 0.75), which is insufficient to fill the entire flower box with a volume of 30 cubic feet. This option underestimates the required amount of soil.
Selecting 27 bags results in a total volume of 20.25 cubic feet (27 × 0.75), which still falls short of the 30 cubic feet needed. This choice also does not provide enough soil to fill the flower box completely.
Opting for 36 bags gives a total volume of 27 cubic feet (36 × 0.75), which is closer but still inadequate for the 30 cubic feet required. This option does not meet the necessary volume to fill the box.
This choice accurately reflects the total volume needed. By calculating 30 cubic feet divided by 0.75 cubic feet per bag, we find that 40 bags are necessary to completely fill the flower box.
The calculation confirms that Violet requires 40 bags of potting soil to fill her flower box, as this quantity precisely matches the total volume of 30 cubic feet. Each incorrect option fails to provide enough soil based on the volume calculations, highlighting the importance of accurate assessment in practical scenarios.
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