6. Yohan bought a new herb planter to go in his long window sill. It is 8 feet long, \( 3 / 4 \) of a foot tall, and \( 2 / 3 \) of a foot wide. (a) How many cubic feet of potting soil will now be required to fill this planter? (b) Potting soil comes in bags that hold \( 3 / 4 \) of a cubic foot of soil. How many bags must be purchased? (c) Will there be any potting soil leftover after the planter is full? (d) If each bag of potting soil was \( \$ 4.67 \) at the hardware store, and the planter itself was \( \$ 15.42 \), how much did Yohan pay?

To find the volume of Yohan's herb planter: (a) The volume of the planter can be calculated using the formula for the volume of a rectangular prism: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \] So, substituting Yohan's measurements: \[ \text{Volume} = 8 \, \text{ft} \times \left( \frac{2}{3} \, \text{ft} \right) \times \left( \frac{3}{4} \, \text{ft} \right) \] \[ \text{Volume} = 8 \times \frac{2}{3} \times \frac{3}{4} = 4 \, \text{cubic feet} \] (b) Since each bag of potting soil holds \( \frac{3}{4} \) cubic feet, we can determine the number of bags needed by dividing the volume of the planter by the volume of one bag: \[ \text{Number of Bags} = \frac{4 \, \text{cubic feet}}{\frac{3}{4} \, \text{cubic feet per bag}} = 4 \times \frac{4}{3} = \frac{16}{3} \approx 5.33 \] So, Yohan needs 6 bags since they can't buy a fraction of a bag! (c) The total volume of soil Yohan will have with 6 bags is: \[ 6 \times \frac{3}{4} = \frac{18}{4} = 4.5 \, \text{cubic feet} \] Since Yohan's planter only requires 4 cubic feet, he will have: \[ 4.5 - 4 = 0.5 \, \text{cubic feet} \] So yes, there will be some leftover potting soil! (d) Now, let's calculate the total cost Yohan spent. The cost of the potting soil is: \[ 6 \, \text{bags} \times 4.67 = 28.02 \] Adding the cost of the planter: \[ 28.02 + 15.42 = 43.44 \] So, Yohan paid a total of \( \$ 43.44 \).