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Sagot :
Desi's error lies in the volume calculations of the calculator and the car's trunk. Here's a step-by-step detailed solution to identify the correct volumes and the mistakes Desi made:
### Step 1: Volume of Calculator
The calculator dimensions are provided:
- Width: [tex]\(3\)[/tex] inches
- Height: [tex]\(4\)[/tex] inches
- Thickness: [tex]\(0.5\)[/tex] inch
The volume [tex]\(V\)[/tex] of a rectangular prism is calculated as:
[tex]\[ V = \text{Width} \times \text{Height} \times \text{Thickness} \][/tex]
Substituting the values:
[tex]\[ V_{\text{calculator}} = 3 \text{ in} \times 4 \text{ in} \times 0.5 \text{ in} = 6 \text{ in}^3 \][/tex]
Desi incorrectly estimated the volume to be [tex]\(60 \text{ in}^3\)[/tex]. The correct volume is [tex]\(6 \text{ in}^3\)[/tex].
### Step 2: Volume of Trunk
The trunk dimensions are provided in feet, so we need to convert them to inches, since 1 foot equals 12 inches:
- Width: [tex]\(4\)[/tex] feet [tex]\(12\)[/tex] inches/foot = [tex]\(48\)[/tex] inches
- Depth: [tex]\(3\)[/tex] feet [tex]\(12\)[/tex] inches/foot = [tex]\(36\)[/tex] inches
- Height: [tex]\(2\)[/tex] feet * [tex]\(12\)[/tex] inches/foot = [tex]\(24\)[/tex] inches
Now, we calculate the volume:
[tex]\[ V = \text{Width} \times \text{Depth} \times \text{Height} \][/tex]
Substituting the values:
[tex]\[ V_{\text{trunk}} = 48 \text{ in} \times 36 \text{ in} \times 24 \text{ in} = 41472 \text{ in}^3 \][/tex]
Desi's estimated trunk volume is correctly noted as [tex]\(41,472 \text{ in}^3\)[/tex].
### Step 3: Number of Calculators that Fit in the Trunk
To find out how many calculators can fit in the trunk, we divide the volume of the trunk by the volume of a calculator:
[tex]\[ \text{Number of calculators} = \frac{\text{Volume of trunk}}{\text{Volume of calculator}} \][/tex]
Substituting the correct values:
[tex]\[ \text{Number of calculators} = \frac{41472 \text{ in}^3}{6 \text{ in}^3} = 6912 \][/tex]
Desi made a calculation error in using the calculator's volume:
[tex]\[ \frac{4 \times 10^4}{6 \times 10^1} \][/tex]
This error led him to calculate that only 667 calculators would fit. Using the correct volume of the calculator yields:
[tex]\[ \frac{41472 \text{ in}^3}{6 \text{ in}^3} = 6912 \][/tex]
### Conclusion
Desi's primary error was incorrectly estimating the volume of the calculator as [tex]\(60 \text{ in}^3\)[/tex]. The correct volume of the calculator is [tex]\(6 \text{ in}^3\)[/tex]. Thus, the correct answer is:
The volume of the calculator is not about [tex]$60 \text{ in}^3$[/tex]. This miscalculation led to the incorrect number of calculators fitting in the trunk.
### Step 1: Volume of Calculator
The calculator dimensions are provided:
- Width: [tex]\(3\)[/tex] inches
- Height: [tex]\(4\)[/tex] inches
- Thickness: [tex]\(0.5\)[/tex] inch
The volume [tex]\(V\)[/tex] of a rectangular prism is calculated as:
[tex]\[ V = \text{Width} \times \text{Height} \times \text{Thickness} \][/tex]
Substituting the values:
[tex]\[ V_{\text{calculator}} = 3 \text{ in} \times 4 \text{ in} \times 0.5 \text{ in} = 6 \text{ in}^3 \][/tex]
Desi incorrectly estimated the volume to be [tex]\(60 \text{ in}^3\)[/tex]. The correct volume is [tex]\(6 \text{ in}^3\)[/tex].
### Step 2: Volume of Trunk
The trunk dimensions are provided in feet, so we need to convert them to inches, since 1 foot equals 12 inches:
- Width: [tex]\(4\)[/tex] feet [tex]\(12\)[/tex] inches/foot = [tex]\(48\)[/tex] inches
- Depth: [tex]\(3\)[/tex] feet [tex]\(12\)[/tex] inches/foot = [tex]\(36\)[/tex] inches
- Height: [tex]\(2\)[/tex] feet * [tex]\(12\)[/tex] inches/foot = [tex]\(24\)[/tex] inches
Now, we calculate the volume:
[tex]\[ V = \text{Width} \times \text{Depth} \times \text{Height} \][/tex]
Substituting the values:
[tex]\[ V_{\text{trunk}} = 48 \text{ in} \times 36 \text{ in} \times 24 \text{ in} = 41472 \text{ in}^3 \][/tex]
Desi's estimated trunk volume is correctly noted as [tex]\(41,472 \text{ in}^3\)[/tex].
### Step 3: Number of Calculators that Fit in the Trunk
To find out how many calculators can fit in the trunk, we divide the volume of the trunk by the volume of a calculator:
[tex]\[ \text{Number of calculators} = \frac{\text{Volume of trunk}}{\text{Volume of calculator}} \][/tex]
Substituting the correct values:
[tex]\[ \text{Number of calculators} = \frac{41472 \text{ in}^3}{6 \text{ in}^3} = 6912 \][/tex]
Desi made a calculation error in using the calculator's volume:
[tex]\[ \frac{4 \times 10^4}{6 \times 10^1} \][/tex]
This error led him to calculate that only 667 calculators would fit. Using the correct volume of the calculator yields:
[tex]\[ \frac{41472 \text{ in}^3}{6 \text{ in}^3} = 6912 \][/tex]
### Conclusion
Desi's primary error was incorrectly estimating the volume of the calculator as [tex]\(60 \text{ in}^3\)[/tex]. The correct volume of the calculator is [tex]\(6 \text{ in}^3\)[/tex]. Thus, the correct answer is:
The volume of the calculator is not about [tex]$60 \text{ in}^3$[/tex]. This miscalculation led to the incorrect number of calculators fitting in the trunk.
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