Astudent measures the diameter of a small cylindrical object and gets the following readings: 4.32, 4.35, 4.31, 4.36, 4.37, 4.34 cm (a) what is the average diameter from these readings? (b) what is the standard deviation of these measurements? the student also measured the length of the object to be (0.126 ± 0.005) m and the mass to be object to be (1.66 ± 0.05) kg. using the method from this week's lab, determine (c) the density and (d) the proportion of error in the density calculation.

a.

b.

c.

Explanation:

a) The average of this values is the sum each number divided by the total number of values.

b) The standard deviation equations is:

If we put all this values in that equation we will get:

Then the mean diameter will be:

c) We know that the density is the mass divided by the volume (ρ = m/V)

and we know that the volume of a cylinder is:

Then:

Using the values that we have, we can calculate the value of density:

We need to use propagation of error to find the error of the density.

Let's find each partial derivative:

1.

2.  

3.

Therefore:

So the density is:

I hope it helps you!

the answer is c. the lower legs are levers, and the knees are fulcrums. the ankles hold the loads.