Question 7 You want to put a 4 inch thick layer of topsoil for a new 25 ft by 32 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of \( 1 / 4 \) cubic yards. \( \overline{\text { Blank } 1} \) cubic yards

To determine how many cubic yards of topsoil you need for the garden, we can follow these steps: 1. **Convert the thickness of the topsoil from inches to feet.** - Since there are 12 inches in a foot, a 4-inch layer of topsoil is: \[ \text{Thickness in feet} = \frac{4 \text{ inches}}{12 \text{ inches/foot}} = \frac{1}{3} \text{ feet} \] 2. **Calculate the volume of topsoil needed in cubic feet.** - The volume \( V \) of the topsoil can be calculated using the formula for the volume of a rectangular prism: \[ V = \text{length} \times \text{width} \times \text{height} \] - Substituting the values: \[ V = 25 \text{ ft} \times 32 \text{ ft} \times \frac{1}{3} \text{ ft} \] 3. **Calculate the volume in cubic feet.** - Performing the multiplication: \[ V = 25 \times 32 \times \frac{1}{3} = \frac{800}{3} \text{ cubic feet} \] 4. **Convert cubic feet to cubic yards.** - There are 27 cubic feet in a cubic yard, so we convert the volume: \[ V_{\text{cubic yards}} = \frac{V_{\text{cubic feet}}}{27} = \frac{\frac{800}{3}}{27} = \frac{800}{81} \text{ cubic yards} \] 5. **Calculate the numerical value.** - Now, we will calculate \( \frac{800}{81} \): \[ \frac{800}{81} \approx 9.87654321 \text{ cubic yards} \] 6. **Round up to the nearest increment of \( \frac{1}{4} \) cubic yards.** - The nearest quarter increment to \( 9.87654321 \) is \( 10 \) cubic yards since \( 9.75 \) is the last quarter increment below it. Thus, you will need to order \( \overline{10} \) cubic yards of topsoil.