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 50%
Well, well, well! It seems like we have a math problem on our hands, don't we? Let me tell you, finding the greatest possible percent error in the volume of a prism can be quite a mathematical roller coaster. Hang on tight!
To calculate the percent error, we need to find the difference between the measured volume and the maximum or minimum possible volume, divide it by the measured volume, and then multiply it by 100 to get a percentage.
Now, the formula for calculating the volume of a rectangular prism is length times width times height. So, let's compute the different volumes:
Measured Volume = 10 * 7 * 5 = 350
Minimum Volume = 9.5 * 6.5 * 4.5 = 275.625
Maximum Volume = 10.5 * 7.5 * 5.5 = 408.375
To find the greatest possible percent error, we compare the difference between the measured and maximum volume:
Difference = |Measured Volume - Maximum Volume| = |350 - 408.375| = 58.375
Now, we divide this difference by the measured volume:
Percent Error = (Difference / Measured Volume) * 100 = (58.375 / 350) * 100 = 16.6786...%
So, my dear friend, the greatest possible percent error in finding the volume of the prism is approximately 16.68%. I hope this clown math has brought a smile to your face!
To calculate the greatest possible percent error in finding the volume of the prism, we need to determine the maximum and minimum volumes based on the given dimensions.
The formula to calculate the volume of a rectangular prism is V = length * width * height.
Measured dimensions:
Length = 10
Width = 7
Height = 5
Minimum dimensions:
Length = 9.5
Width = 6.5
Height = 4.5
Maximum dimensions:
Length = 10.5
Width = 7.5
Height = 5.5
Now, we can calculate the volume of the prism using both the minimum and maximum dimensions:
Minimum volume = 9.5 * 6.5 * 4.5 = 275.625
Maximum volume = 10.5 * 7.5 * 5.5 = 423.75
To find the greatest possible percent error, we need to compare the difference between the maximum and minimum volumes with the measured volume:
Difference = Maximum volume - Minimum volume = 423.75 - 275.625 = 148.125
Now, we can calculate the percent error:
Percent Error = (Difference / Measured volume) * 100
= (148.125 / (10 * 7 * 5)) * 100
= 29.625%
Therefore, the greatest possible percent error in finding the volume of the prism is approximately 29.63%, rounded to the nearest percent.
To determine the greatest possible percent error in finding the volume of the prism, we need to consider the measured dimensions and the minimum and maximum possible dimensions based on the greatest possible error.
First, let's calculate the volume using the measured dimensions:
Volume (measured) = Length x Width x Height
= 10 x 7 x 5
= 350 cubic units
Next, let's calculate the minimum and maximum volumes based on the minimum and maximum possible dimensions:
Minimum Volume = Length(minimum) x Width(minimum) x Height(minimum)
= 9.5 x 6.5 x 4.5
= 280.875 cubic units
Maximum Volume = Length(maximum) x Width(maximum) x Height(maximum)
= 10.5 x 7.5 x 5.5
= 408.375 cubic units
Now, let's calculate the percent error for both the minimum and maximum volumes:
Percent Error = (|Volume (measured) - Volume (minimum or maximum)| / Volume (measured)) x 100
For the minimum volume:
Percent Error (minimum) = (|350 - 280.875| / 350) x 100
= (69.125 / 350) x 100
= 0.197 x 100
= 19.7%
For the maximum volume:
Percent Error (maximum) = (|350 - 408.375| / 350) x 100
= (58.375 / 350) x 100
= 0.167 x 100
= 16.7%
The greatest possible percent error would be the higher value between the two, which is 19.7%. Therefore, the greatest possible percent error in finding the volume of the prism is approximately 19.7%, not 50%.