Sure! Let's find the volume of a pipe with a diameter of 50 mm and a length of 0.9 m, using the value of π as 3.142.
### Step 1: Convert the Diameter to Meters
The given diameter of the pipe is 50 mm. To convert this into meters, we use the conversion factor:
1 meter = 1000 millimeters.
So,
[tex]\[ \text{diameter in meters} = \frac{50 \, \text{mm}}{1000} = 0.05 \, \text{m} \][/tex]
### Step 2: Find the Radius of the Pipe
The radius is half of the diameter. Therefore,
[tex]\[ \text{radius} = \frac{\text{diameter}}{2} = \frac{0.05 \, \text{m}}{2} = 0.025 \, \text{m} \][/tex]
### Step 3: Calculate the Cross-Sectional Area
The cross-sectional area [tex]\(A\)[/tex] of the pipe (which is a circle) is given by the formula:
[tex]\[ A = \pi \times (\text{radius})^2 \][/tex]
Substituting the values, we get:
[tex]\[ A = 3.142 \times (0.025 \, \text{m})^2 \][/tex]
[tex]\[ A = 3.142 \times 0.000625 \, \text{m}^2 \][/tex]
[tex]\[ A = 0.00196375 \, \text{m}^2 \][/tex]
### Step 4: Calculate the Volume of the Pipe
The volume [tex]\(V\)[/tex] of the pipe is given by the formula:
[tex]\[ V = \text{cross-sectional area} \times \text{length} \][/tex]
So,
[tex]\[ V = 0.00196375 \, \text{m}^2 \times 0.9 \, \text{m} \][/tex]
[tex]\[ V = 0.001767375 \, \text{m}^3 \][/tex]
Therefore, the volume of the pipe is [tex]\(0.001767375 \, \text{m}^3\)[/tex].
