You want to put a 3 inch thick layer of topsoil for a new 17 ft by 22 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.

To determine how many cubic yards of topsoil you'll need to order, we need to calculate the volume of soil required for your garden in cubic feet and then convert that volume to cubic yards.

### Step 1: Calculate the volume in cubic feet.
The garden's dimensions are 17 feet by 22 feet, and you want a 3-inch thick layer of topsoil.

- **Area of the garden**:  
  \[
  \text{Area} = 17 \times 22 = 374 \text{ square feet}
  \]
  
- **Thickness of the soil layer**:  
  Convert 3 inches to feet (since we want the volume in cubic feet):
  \[
  \text{Thickness} = \frac{3}{12} = 0.25 \text{ feet}
  \]

- **Volume in cubic feet**:  
  \[
  \text{Volume} = \text{Area} \times \text{Thickness} = 374 \times 0.25 = 93.5 \text{ cubic feet}
  \]

### Step 2: Convert cubic feet to cubic yards.
There are 27 cubic feet in one cubic yard.

\[
\text{Volume in cubic yards} = \frac{93.5}{27} \approx 3.46 \text{ cubic yards}
\]

### Step 3: Round to the nearest increment the store sells.
Since the store sells in increments of 1/4 cubic yard, round 3.46 to the nearest 1/4 cubic yard:

\[
\text{Rounded volume} = 3.5 \text{ cubic yards}
\]

### Final Answer:
You need to order **3.5 cubic yards** of topsoil.

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you calculate the area of a different-shaped garden, like a circle or triangle?
2. What if the garden had varying thicknesses of soil required?
3. How does the conversion factor from cubic feet to cubic yards affect large projects?
4. How would the calculation change if the garden were on a slope?
5. What are some factors to consider when purchasing soil, such as quality or type?

**Tip:** When planning a garden, it's useful to account for some extra soil to cover any settling or leveling needs that may arise.

Learn how to calculate the volume of topsoil needed for a garden with dimensions 17 ft by 22 ft and a depth of 3 inches. This guide covers geometric concepts, measurement conversions, and provides a detailed step-by-step solution. Suitable for students in Grades 6-8.

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