Measurement Value length 31.3 ± 0.2 cm width 12.8 ± 0.2 cm height 8.9 ± 0.2 cm Y
ID: 3196113 • Letter: M
Question
Measurement Value length 31.3 ± 0.2 cm width 12.8 ± 0.2 cm height 8.9 ± 0.2 cm
Your measurements of a sample brick. You are working for a construction company and are in charge of ordering supplies for some new brick houses that are going to be built. The company you are considering for supplying the bricks sends you a sample. You want to decide if the brick has the appropriate volume. You observe that it is roughly in the shape of a rectangular prism so you take measurements of its length, width, and height. The results are found in Table 5.3. You realize that it would be a good idea to determine the volume using a second method as well. Then you could decide if the two results were consistent. If they were, then you know you could be confident with your determination of the volume of the brick. As a second method, you take a large plastic graduated cylinder and fill it up partially with water. You measure the water level to be 2720 ± 50 mL. You then submerge the brick in the water. You measure the water level now to be 6110 ± 50 mL.
3. For each of the methods, describe an assumption that the method makes.
4. For each of the assumptions in the previous question, determine if the assumption tends to make the calculated volume smaller, larger, or randomly different than the actual volume. Explain your reasoning.
Explanation / Answer
1)Volume by measuring gauge
V = 31.3(12.8)(8.9)
V = 3565.696 ± 0.008 cm³
the volume by dunking is found knowing 1 ml = 1cm³
V = 6110 - 2720
V = 3390 ± 50 cm³
2) The two volume calculations are not consistant
3) The first method only measures the gross exterior dimensions of the block and ignores any curvatures or holes within the block.
the precision given for the dunking method seems out of sorts with the precision of the reported numbers. If one only had confidence to ±50ml then one would only expect to find measurement precision to the hundreds place, not the tens place as reported. If measuring to the tens place then precision might be expected to be ±5 ml unless the graduations are stated that 50 ml is the tolerance limit which just indicated an imprecise construction method for the graduated beaker.
4)If consistency occured one might have concluded that either method would give a similar result and there are no un accounted for assumptions.