Question
The bed of a pick up truck with a cover has a length of 8 feet width of 10 feet and height of 2 feet. You are packing as many moving boxes into the truck as you can. Each box has a length of 2 feet, a width of 2 feet and a height of 1.5. If you fit 20 boxes into the truck, how much space are you NOT using if the cover is on the bed of the pick up truck?
Question 11 options:
10%
54%
70%
25%
Question 11 options:
10%
54%
70%
25%
Answers
Answered by
GPT-4o mini
To determine how much space is not being used when packing the boxes into the truck, we can follow these steps:
1. **Calculate the volume of the truck bed**:
The volume \( V \) of a rectangular prism (which is the shape of the truck bed) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
The dimensions of the truck bed are:
- Length = 8 feet
- Width = 10 feet
- Height = 2 feet
Therefore, the volume of the truck bed is:
\[
V_{\text{truck}} = 8 \, \text{ft} \times 10 \, \text{ft} \times 2 \, \text{ft} = 160 \, \text{cubic feet}
\]
2. **Calculate the volume of one moving box**:
The dimensions of each box are:
- Length = 2 feet
- Width = 2 feet
- Height = 1.5 feet
Therefore, the volume of one box is:
\[
V_{\text{box}} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.5 \, \text{ft} = 6 \, \text{cubic feet}
\]
3. **Calculate the total volume of 20 boxes**:
If you fit 20 boxes into the truck, the total volume occupied by the boxes is:
\[
V_{\text{20 boxes}} = 20 \times V_{\text{box}} = 20 \times 6 \, \text{cubic feet} = 120 \, \text{cubic feet}
\]
4. **Calculate the unused space in the truck bed**:
To find the unused space in the truck bed, subtract the volume occupied by the boxes from the volume of the truck bed:
\[
\text{Unused space} = V_{\text{truck}} - V_{\text{20 boxes}} = 160 \, \text{cubic feet} - 120 \, \text{cubic feet} = 40 \, \text{cubic feet}
\]
5. **Calculate the percentage of unused space**:
To find the percentage of the space that is not used, we use the formula:
\[
\text{Unused space percentage} = \left( \frac{\text{Unused space}}{V_{\text{truck}}} \right) \times 100 = \left( \frac{40}{160} \right) \times 100 = 25\%
\]
Thus, the amount of space you are NOT using in the truck is **25%**.
The answer is: **25%**.
1. **Calculate the volume of the truck bed**:
The volume \( V \) of a rectangular prism (which is the shape of the truck bed) can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
The dimensions of the truck bed are:
- Length = 8 feet
- Width = 10 feet
- Height = 2 feet
Therefore, the volume of the truck bed is:
\[
V_{\text{truck}} = 8 \, \text{ft} \times 10 \, \text{ft} \times 2 \, \text{ft} = 160 \, \text{cubic feet}
\]
2. **Calculate the volume of one moving box**:
The dimensions of each box are:
- Length = 2 feet
- Width = 2 feet
- Height = 1.5 feet
Therefore, the volume of one box is:
\[
V_{\text{box}} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.5 \, \text{ft} = 6 \, \text{cubic feet}
\]
3. **Calculate the total volume of 20 boxes**:
If you fit 20 boxes into the truck, the total volume occupied by the boxes is:
\[
V_{\text{20 boxes}} = 20 \times V_{\text{box}} = 20 \times 6 \, \text{cubic feet} = 120 \, \text{cubic feet}
\]
4. **Calculate the unused space in the truck bed**:
To find the unused space in the truck bed, subtract the volume occupied by the boxes from the volume of the truck bed:
\[
\text{Unused space} = V_{\text{truck}} - V_{\text{20 boxes}} = 160 \, \text{cubic feet} - 120 \, \text{cubic feet} = 40 \, \text{cubic feet}
\]
5. **Calculate the percentage of unused space**:
To find the percentage of the space that is not used, we use the formula:
\[
\text{Unused space percentage} = \left( \frac{\text{Unused space}}{V_{\text{truck}}} \right) \times 100 = \left( \frac{40}{160} \right) \times 100 = 25\%
\]
Thus, the amount of space you are NOT using in the truck is **25%**.
The answer is: **25%**.