Question
a delivery truck needs service needs to transport 75 boxes. The boxes are all cubed with a side length of 18 inches.
Answers
Answered by
GPT-4o mini
To determine if the delivery truck can transport the 75 boxes, we need to calculate the total volume of the boxes and potentially the space required for transportation, depending on the truck's dimensions. Let's break it down:
### Step 1: Calculate the volume of a single box
Each box is a cube with a side length of 18 inches. The volume \( V \) of a cube is given by the formula:
\[
V = a^3
\]
where \( a \) is the side length.
Substituting the side length:
\[
V = 18 \, \text{inches} \times 18 \, \text{inches} \times 18 \, \text{inches} = 5832 \, \text{cubic inches}
\]
### Step 2: Calculate the total volume of 75 boxes
To find the total volume for 75 boxes:
\[
\text{Total Volume} = \text{Volume of one box} \times \text{Number of boxes}
\]
\[
\text{Total Volume} = 5832 \, \text{cubic inches} \times 75 = 437400 \, \text{cubic inches}
\]
### Step 3: Convert the total volume to cubic feet (if needed)
Since there are 1728 cubic inches in a cubic foot (12 inches x 12 inches x 12 inches):
\[
\text{Total Volume in cubic feet} = \frac{437400 \, \text{cubic inches}}{1728 \, \text{cubic inches per cubic foot}} \approx 252.1 \, \text{cubic feet}
\]
### Step 4: Assess truck capacity
To determine if the delivery truck can safely transport these boxes, you will need to compare the total volume calculated with the cargo capacity of the truck you're using. If you have the dimensions or the capacity of the delivery truck, you can verify whether it can accommodate at least 252.1 cubic feet.
If you have specific truck dimensions or capacity, please provide that information for further analysis.
### Step 1: Calculate the volume of a single box
Each box is a cube with a side length of 18 inches. The volume \( V \) of a cube is given by the formula:
\[
V = a^3
\]
where \( a \) is the side length.
Substituting the side length:
\[
V = 18 \, \text{inches} \times 18 \, \text{inches} \times 18 \, \text{inches} = 5832 \, \text{cubic inches}
\]
### Step 2: Calculate the total volume of 75 boxes
To find the total volume for 75 boxes:
\[
\text{Total Volume} = \text{Volume of one box} \times \text{Number of boxes}
\]
\[
\text{Total Volume} = 5832 \, \text{cubic inches} \times 75 = 437400 \, \text{cubic inches}
\]
### Step 3: Convert the total volume to cubic feet (if needed)
Since there are 1728 cubic inches in a cubic foot (12 inches x 12 inches x 12 inches):
\[
\text{Total Volume in cubic feet} = \frac{437400 \, \text{cubic inches}}{1728 \, \text{cubic inches per cubic foot}} \approx 252.1 \, \text{cubic feet}
\]
### Step 4: Assess truck capacity
To determine if the delivery truck can safely transport these boxes, you will need to compare the total volume calculated with the cargo capacity of the truck you're using. If you have the dimensions or the capacity of the delivery truck, you can verify whether it can accommodate at least 252.1 cubic feet.
If you have specific truck dimensions or capacity, please provide that information for further analysis.