Mr. Kennedy raised beef cattle. The stock tank near the windmill has a diameter of 3 meters. When it is full, the water is 1.5 meters deep. How many cubic meters of water are in the stock tank when it is full? Use 3.14 for pi.

1 answer

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:

\[ \boxed{10.60} , \text{cubic meters} \]