The table on the right shows the measured dimensions of a rectangular prism and the minimum and maximum possible dimensions based on the greatest possible error. What is the greatest possible percent error in finding the volume of the prism? (Round to the nearest percent as needed.)
Length|Width|Height
Measured:10 | 7 | 5
Minimum: 9.5 | 6.5 | 4.5
Maximum:10.5 | 7.5 | 5.5
I said the greatest possible percent error in finding the volume of the prism is 3%.
The greatest possible percent error is
26%.
Hello fellow peasent, if it 5%
Well, well, well! It seems we have a classic case of prism measuring here. Let's see if we can crack this puzzle and find the greatest possible percent error in finding the volume.
To find the percent error, we need to calculate the difference between the measured volume and the maximum volume, divided by the measured volume, then multiplied by 100.
Measured Volume = Length * Width * Height
Max Volume = Max Length * Max Width * Max Height
Measured Volume = 10 * 7 * 5 = 350
Max Volume = 10.5 * 7.5 * 5.5 = 423.75
Difference = Max Volume - Measured Volume = 423.75 - 350 = 73.75
Percent Error = (Difference / Measured Volume) * 100
Percent Error = (73.75 / 350) * 100 = 21.07%
So, my friend, the greatest possible percent error in finding the volume of the prism is approximately 21%. Keep in mind that this calculation assumes you made some serious measurement blunders. Let's hope for the sake of geometry that you didn't have a moment of "I don't prism-ly know what I'm doing!"
To calculate the maximum possible percent error in finding the volume of the rectangular prism, we need to compare the maximum and minimum values for each dimension and determine the maximum possible difference in volume.
Given:
Measured length = 10
Measured width = 7
Measured height = 5
Minimum length = 9.5
Minimum width = 6.5
Minimum height = 4.5
Maximum length = 10.5
Maximum width = 7.5
Maximum height = 5.5
To find the maximum possible difference in volume, we need to find the maximum and minimum volumes of the prism.
Minimum volume = Minimum length × Minimum width × Minimum height
Maximum volume = Maximum length × Maximum width × Maximum height
Minimum volume = 9.5 × 6.5 × 4.5
Maximum volume = 10.5 × 7.5 × 5.5
Now, we can calculate the percent error by taking the difference between the maximum and minimum volumes and dividing it by the measured volume, then multiplying by 100.
Percent error = ((Maximum volume - Minimum volume) / Measured volume) × 100
Percent error = ((10.5 × 7.5 × 5.5) - (9.5 × 6.5 × 4.5)) / (10 × 7 × 5) × 100
Percent error ≈ 3.45%
Therefore, the greatest possible percent error in finding the volume of the prism is approximately 3.45%.
To find the greatest possible percent error in finding the volume of the prism, you can use the formula for percent error:
Percent Error = ((|Measured - Actual|) / Actual) * 100
Since the volume of a rectangular prism is calculated by multiplying the length, width, and height together, you need to find the volume for both the measured dimensions and the minimum and maximum possible dimensions.
Measured volume = length * width * height = 10 * 7 * 5 = 350 cubic units.
Minimum volume = length * width * height = 9.5 * 6.5 * 4.5 ≈ 270.56 cubic units.
Maximum volume = length * width * height = 10.5 * 7.5 * 5.5 ≈ 404.63 cubic units.
Now plug these values into the percent error formula to find the percent error for both the minimum and maximum volumes:
Percent Error (minimum volume) = ((|Measured volume - Minimum volume|) / Minimum volume) * 100 = ((|350 - 270.56|) / 270.56) * 100 ≈ 29.38%
Percent Error (maximum volume) = ((|Measured volume - Maximum volume|) / Maximum volume) * 100 = ((|350 - 404.63|) / 404.63) * 100 ≈ 13.52%
Since you are looking for the greatest possible percent error, you can compare the percent errors for both the minimum and maximum volumes and choose the highest value. In this case, the greatest possible percent error is approximately 29.38%. Therefore, your answer of 3% is incorrect.