Based on your Part 2 answers, how much will it cost to deliver the topsoil? \$ 175 Cost for Pickup You want to compare this to picking up the soil yourself. The truck you have available has a bed that is 80 inches long, 69 inches wide, and 20 inches tall. The store is 6 miles away and it takes about 20 minutes to drive there. The truck averages about 17 miles per gallon and gas costs $$ \$ 3.04 $$ per gallon. What is the volume of topsoil that you can fit in the truck without it spilling over? Round answers to two decimal places, if needed. $$ \square $$ $$ 110400 $$ cubic inches $$ \begin{array}{l} =63.89 \quad \text { cubic feet } \ =2.37 \quad \sim \text { cubic yards } \end{array} $$ How many trips will you need to make in your truck? $$ \square $$ 36 trips in the truck What is the total cost (in gas) to deliver the soil in the pickup truck? $$ \$ $$ $$ \square $$ Enscran integar or debimal number, with 2 trailmal pisces [more]] Comparing Cost for Final Decision Which option is cheaper? use own truck $$ \checkmark \checkmark $$ How much cheaper is it? \$ $$ \square $$ 166.64

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Let's break down the problem step by step to find the total cost of delivering the topsoil using your truck.

### Step 1: Calculate the Volume of the Truck Bed
The volume $$ V $$ of the truck bed can be calculated using the formula for the volume of a rectangular prism:

$$
V = \text{length} \times \text{width} \times \text{height}
$$

Given:
- Length = 80 inches
- Width = 69 inches
- Height = 20 inches

Calculating the volume in cubic inches:

$$
V = 80 \times 69 \times 20
$$

### Step 2: Convert Volume to Cubic Feet and Cubic Yards
To convert cubic inches to cubic feet, use the conversion factor $$ 1 \text{ cubic foot} = 1728 \text{ cubic inches} $$:

$$
\text{Cubic feet} = \frac{V}{1728}
$$

To convert cubic feet to cubic yards, use the conversion factor $$ 1 \text{ cubic yard} = 27 \text{ cubic feet} $$:

$$
\text{Cubic yards} = \frac{\text{Cubic feet}}{27}
$$

### Step 3: Calculate the Number of Trips
Given that the total volume of topsoil needed is $$ 110400 $$ cubic inches, we can find the number of trips required by dividing the total volume by the volume of the truck bed:

$$
\text{Number of trips} = \frac{\text{Total volume}}{\text{Volume of truck bed}}
$$

### Step 4: Calculate the Total Cost of Gas
1. **Distance to the store**: 6 miles (one way), so round trip is $$ 12 $$ miles.
2. **Fuel efficiency**: 17 miles per gallon.
3. **Gas cost**: $$ \$3.04 $$ per gallon.

First, calculate the gallons of gas needed for one round trip:

$$
\text{Gallons needed} = \frac{\text{Total distance}}{\text{Miles per gallon}} = \frac{12}{17}
$$

Then, calculate the cost of gas for one round trip:

$$
\text{Cost of gas for one trip} = \text{Gallons needed} \times \text{Gas cost}
$$

Finally, multiply the cost of gas for one trip by the number of trips to get the total cost of gas.

### Step 5: Compare Costs
Now, we can compare the total cost of using the truck with the cost of delivery $$ \$175 $$ and find out how much cheaper it is to use the truck.

Let's perform the calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{110400}{\left(80\times 69\times 20\right)}$$
- step1: Remove the parentheses:
  $$\frac{110400}{80\times 69\times 20}$$
- step2: Multiply the terms:
  $$\frac{110400}{110400}$$
- step3: Reduce the fraction:
  $$1$$
Calculate or simplify the expression $$ (12/17)*3.04 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{12}{17}\times 3.04$$
- step1: Convert the expressions:
  $$\frac{12}{17}\times \frac{76}{25}$$
- step2: Multiply the fractions:
  $$\frac{12\times 76}{17\times 25}$$
- step3: Multiply the terms:
  $$\frac{912}{17\times 25}$$
- step4: Multiply the terms:
  $$\frac{912}{425}$$
Calculate or simplify the expression $$ 80*69*20 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$80\times 69\times 20$$
- step1: Multiply the terms:
  $$5520\times 20$$
- step2: Multiply the numbers:
  $$110400$$
Calculate or simplify the expression $$ 12/17 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{12}{17}$$
Calculate or simplify the expression $$ (12/17)*3.04*1 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{12}{17}\times 3.04\times 1$$
- step1: Rewrite the expression:
  $$\frac{12}{17}\times 3.04$$
- step2: Convert the expressions:
  $$\frac{12}{17}\times \frac{76}{25}$$
- step3: Multiply the fractions:
  $$\frac{12\times 76}{17\times 25}$$
- step4: Multiply the terms:
  $$\frac{912}{17\times 25}$$
- step5: Multiply the terms:
  $$\frac{912}{425}$$
Calculate or simplify the expression $$ 175 - 2.145882 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$175-2.145882$$
- step1: Subtract the numbers:
  $$172.854118$$
### Summary of Calculations

1. **Volume of the Truck Bed**:
   - The volume of the truck bed is $$ 110400 $$ cubic inches.

2. **Number of Trips**:
   - You will need to make $$ 1 $$ trip to deliver the topsoil.

3. **Total Cost of Gas for One Trip**:
   - The total cost of gas for one round trip is approximately $$ \$2.15 $$.

4. **Comparison of Costs**:
   - The cost of delivery using the truck is $$ \$2.15 $$.
   - The cost of delivery from the store is $$ \$175 $$.
   - The savings by using your own truck is approximately $$ \$172.85 $$.

### Final Answers
- **Total Cost (in gas) to deliver the soil in the pickup truck**: $$ \$2.15 $$
- **How much cheaper is it?**: $$ \$172.85 $$

Thus, using your own truck is significantly cheaper than the delivery option.
Using your own truck costs \$2.15 in gas and saves \$172.85 compared to the delivery option.

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