To find the thickness of the wall of a hollow cylinder given the external and internal diameters, we can follow these steps:
### Step 1: Write down the given values
- External diameter (De) = \(4.23 \pm 0.01\) cm
- Internal diameter (Di) = \(3.89 \pm 0.01\) cm
### Step 2: Calculate the external radius (Re)
The external radius (Re) is half of the external diameter:
\[
Re = \frac{De}{2} = \frac{4.23 \, \text{cm}}{2} = 2.115 \, \text{cm}
\]
To find the uncertainty in the radius, we divide the uncertainty in the diameter by 2:
\[
\Delta Re = \frac{0.01 \, \text{cm}}{2} = 0.005 \, \text{cm}
\]
Thus, the external radius is:
\[
Re = 2.115 \pm 0.005 \, \text{cm
\]
### Step 3: Calculate the internal radius (Ri)
The internal radius (Ri) is half of the internal diameter:
\[
Ri = \frac{Di}{2} = \frac{3.89 \, \text{cm}}{2} = 1.945 \, \text{cm}
\]
Similarly, the uncertainty in the internal radius is:
\[
\Delta Ri = \frac{0.01 \, \text{cm}}{2} = 0.005 \, \text{cm}
\]
Thus, the internal radius is:
\[
Ri = 1.945 \pm 0.005 \, \text{cm}
\]
### Step 4: Calculate the thickness of the wall (t)
The thickness of the wall (t) is the difference between the external radius and the internal radius:
\[
t = Re - Ri = (2.115 \pm 0.005) - (1.945 \pm 0.005)
\]
Calculating the difference:
\[
t = 2.115 - 1.945 = 0.17 \, \text{cm}
\]
### Step 5: Calculate the uncertainty in thickness
To find the uncertainty in thickness, we add the uncertainties of the external and internal radii:
\[
\Delta t = \Delta Re + \Delta Ri = 0.005 + 0.005 = 0.01 \, \text{cm}
\]
### Final Result
Thus, the thickness of the wall of the cylinder is:
\[
t = 0.17 \pm 0.01 \, \text{cm}
\]
