To calculate the volume of water in a cylindrical stock tank when it is full, we can use the formula for the volume \( V \) of a cylinder, which is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height (or depth) of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14.
Step 1: Determine the Radius
The diameter of the stock tank is given as 3 meters. Therefore, the radius \( r \) is half of the diameter:
\[ r = \frac{3 , \text{meters}}{2} = 1.5 , \text{meters} \]
Step 2: Use the Depth as Height
The depth of the water when the tank is full is 1.5 meters. Hence, we have:
\[ h = 1.5 , \text{meters} \]
Step 3: Substitute the Values into the Volume Formula
Now we can substitute the values of \( r \), \( h \), and \( \pi \) into the volume formula:
\[ V = 3.14 \times (1.5)^2 \times 1.5 \]
Calculating \( (1.5)^2 \):
\[ (1.5)^2 = 2.25 \]
Step 4: Complete the Volume Calculation
Now, substituting in:
\[ V = 3.14 \times 2.25 \times 1.5 \]
Calculating \( 3.14 \times 2.25 \):
\[ 3.14 \times 2.25 = 7.065 \]
Now we multiply this result by \( 1.5 \):
\[ V = 7.065 \times 1.5 = 10.5975 \]
Thus, the volume of water in the stock tank when it is full is approximately:
\[ \boxed{10.60} , \text{cubic meters} \]