The table below shows the measured dimensions of a prism, and the maximum and minimum possible values based on the greatest possible error.
Dimensions l w h
Measured 9 5 3
Maximum 9.5 5.5 3.5
Minimum 8.5 4.5 2.5
a. Find the measured volume.
b. Find the maximum volume.
c. Find the minimum volume.
d. What is the percent error? Round to the nearest percent.
I can't figure it out!!!
For a, b and c:
Volume = l * w * h
I'm not sure if this is what you want for d.
Percent error = (min or max volume - measured volume)/measured volume
A volume of a can of 300cm and the heightis 15.92? I need help please
No problem, I can help you! Let's go step-by-step to solve this problem.
a. To find the measured volume, we need to multiply the measured dimensions of the prism. So the measured volume is calculated as follows:
Measured Volume = Measured Length (l) x Measured Width (w) x Measured Height (h)
= 9 x 5 x 3
= 135 cubic units
b. To find the maximum volume, we need to multiply the maximum possible values of each dimension. So the maximum volume is calculated as:
Maximum Volume = Maximum Length (l) x Maximum Width (w) x Maximum Height (h)
= 9.5 x 5.5 x 3.5
= 182.875 cubic units (rounded to three decimal places)
c. To find the minimum volume, we need to multiply the minimum possible values of each dimension. So the minimum volume is calculated as:
Minimum Volume = Minimum Length (l) x Minimum Width (w) x Minimum Height (h)
= 8.5 x 4.5 x 2.5
= 95.625 cubic units (rounded to three decimal places)
d. To calculate the percent error, we need to find the difference between the measured volume and the maximum volume, divide it by the measured volume, and then multiply by 100. The formula for percent error is:
Percent Error = |Measured Volume - Maximum Volume| / Measured Volume * 100
Using the values we calculated above:
Percent Error = |135 - 182.875| / 135 * 100
= 47.875 / 135 * 100
= 35.5% (rounded to the nearest percent)
So the percent error is approximately 35.5%.
To find the volume of the prism, we need to multiply the three dimensions together. Let's go through each question step by step.
a. To find the measured volume, use the measured dimensions of the prism:
Measured Volume = measured length * measured width * measured height
Measured Volume = 9 * 5 * 3
Measured Volume = 135 cubic units
So, the measured volume of the prism is 135 cubic units.
b. To find the maximum volume, use the maximum dimensions:
Maximum Volume = maximum length * maximum width * maximum height
Maximum Volume = 9.5 * 5.5 * 3.5
Maximum Volume = 183.75 cubic units
Thus, the maximum volume of the prism is 183.75 cubic units.
c. To find the minimum volume, use the minimum dimensions:
Minimum Volume = minimum length * minimum width * minimum height
Minimum Volume = 8.5 * 4.5 * 2.5
Minimum Volume = 95.625 cubic units
Therefore, the minimum volume of the prism is 95.625 cubic units.
d. To calculate the percent error, you need to find the difference between the maximum and minimum volumes and then divide it by the measured volume:
Difference = Maximum Volume - Minimum Volume
Difference = 183.75 - 95.625
Difference = 88.125 cubic units
Percent Error = (Difference / Measured Volume) * 100
Percent Error = (88.125 / 135) * 100
Percent Error ≈ 65.28%
Hence, the percent error is approximately 65.28% when rounded to the nearest percent.