Answer :
To find the greatest possible percent error in calculating the volume of the prism, let's walk through the following steps:
1. Determine the measured volume of the prism:
- Measured dimensions: Length = 10, Width = 6, Height = 4.
- The formula for the volume of a rectangular prism is \( V = \text{Length} \times \text{Width} \times \text{Height} \).
- Plugging in the measured dimensions:
[tex]\[ V_{\text{measured}} = 10 \times 6 \times 4 = 240 \][/tex]
2. Determine the minimum possible volume of the prism:
- Minimum dimensions: Length = 9.5, Width = 5.5, Height = 3.5.
- Using the volume formula:
[tex]\[ V_{\text{min}} = 9.5 \times 5.5 \times 3.5 = 182.875 \][/tex]
3. Determine the maximum possible volume of the prism:
- Maximum dimensions: Length = 10.5, Width = 6.5, Height = 4.5.
- Using the volume formula:
[tex]\[ V_{\text{max}} = 10.5 \times 6.5 \times 4.5 = 307.125 \][/tex]
4. Calculate the error in the volume:
- The error in volume is determined by the difference between the maximum and minimum volumes.
[tex]\[ \text{Error in Volume} = V_{\text{max}} - V_{\text{min}} = 307.125 - 182.875 = 124.25 \][/tex]
5. Calculate the percent error based on the measured volume:
- The percent error is calculated by dividing the error in volume by the measured volume and then multiplying by 100 to get a percentage.
[tex]\[ \text{Percent Error} = \left( \frac{\text{Error in Volume}}{V_{\text{measured}}} \right) \times 100 = \left( \frac{124.25}{240} \right) \times 100 \approx 51.77\% \][/tex]
Thus, the greatest possible percent error in finding the volume of the prism is approximately [tex]\( 51.77\% \)[/tex].
1. Determine the measured volume of the prism:
- Measured dimensions: Length = 10, Width = 6, Height = 4.
- The formula for the volume of a rectangular prism is \( V = \text{Length} \times \text{Width} \times \text{Height} \).
- Plugging in the measured dimensions:
[tex]\[ V_{\text{measured}} = 10 \times 6 \times 4 = 240 \][/tex]
2. Determine the minimum possible volume of the prism:
- Minimum dimensions: Length = 9.5, Width = 5.5, Height = 3.5.
- Using the volume formula:
[tex]\[ V_{\text{min}} = 9.5 \times 5.5 \times 3.5 = 182.875 \][/tex]
3. Determine the maximum possible volume of the prism:
- Maximum dimensions: Length = 10.5, Width = 6.5, Height = 4.5.
- Using the volume formula:
[tex]\[ V_{\text{max}} = 10.5 \times 6.5 \times 4.5 = 307.125 \][/tex]
4. Calculate the error in the volume:
- The error in volume is determined by the difference between the maximum and minimum volumes.
[tex]\[ \text{Error in Volume} = V_{\text{max}} - V_{\text{min}} = 307.125 - 182.875 = 124.25 \][/tex]
5. Calculate the percent error based on the measured volume:
- The percent error is calculated by dividing the error in volume by the measured volume and then multiplying by 100 to get a percentage.
[tex]\[ \text{Percent Error} = \left( \frac{\text{Error in Volume}}{V_{\text{measured}}} \right) \times 100 = \left( \frac{124.25}{240} \right) \times 100 \approx 51.77\% \][/tex]
Thus, the greatest possible percent error in finding the volume of the prism is approximately [tex]\( 51.77\% \)[/tex].
