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40 bags of potting soil are needed to fill the flower box.

To determine the number of bags of potting soil required, we first calculate the volume of the flower box, which is 30 cubic feet. Given that each bag contains 0.75 cubic feet of soil, dividing the total volume by the volume per bag (30 ÷ 0.75) results in 40 bags needed.

A) 24

This option is incorrect as it underestimates the total volume of soil required. If Violet were to use only 24 bags, the total volume of soil would only be 18 cubic feet (24 x 0.75), which is insufficient to fill the flower box completely.

B) 27

Option B is also incorrect because 27 bags of potting soil would only provide 20.25 cubic feet of soil (27 x 0.75). This amount is still less than the required volume of 30 cubic feet, leaving the flower box partially filled.

C) 36

This option is incorrect as well. If Violet used 36 bags, she would have a total of 27 cubic feet of soil (36 x 0.75). This volume is still not enough to fill the flower box, falling short by 3 cubic feet.

D) 40

This is the correct option. Using 40 bags of potting soil provides exactly 30 cubic feet of soil (40 x 0.75), which matches the volume of the flower box perfectly, ensuring it is completely filled.

Conclusion

The calculation confirms that 40 bags are required to fill the flower box, as it provides the exact volume needed. All other options fall short of the necessary volume, making them unsuitable for this task. Thus, D is the only correct choice.