Certainly! Let's solve the problem step-by-step.
### Calculation of the Volume of the Water Tank
#### Step 1: Calculate the Radius of the Tank
The diameter of the tank is given as 3.5 meters. The radius ([tex]\(r\)[/tex]) is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{3.5 \, \text{m}}{2} = 1.75 \, \text{m} \][/tex]
#### Step 2: Calculate the Volume of the Tank in Cubic Meters
The tank is cylindrical in shape, and the formula for the volume ([tex]\(V\)[/tex]) of a cylinder is:
[tex]\[ V = \pi \times r^2 \times h \][/tex]
Where:
- [tex]\(\pi = 3.14\)[/tex]
- [tex]\(r = 1.75 \, \text{m}\)[/tex]
- [tex]\(h = 5 \, \text{m}\)[/tex]
Let's calculate:
[tex]\[ V = 3.14 \times (1.75)^2 \times 5 \][/tex]
First, calculate [tex]\(r^2\)[/tex]:
[tex]\[ r^2 = (1.75)^2 = 3.0625 \][/tex]
Next, multiply by [tex]\(\pi\)[/tex] and the height:
[tex]\[ V = 3.14 \times 3.0625 \times 5 = 48.08125 \, \text{m}^3 \][/tex]
#### Step 3: Convert the Volume to Liters
We know that:
[tex]\[ 1 \, \text{m}^3 = 1000 \, \text{liters} \][/tex]
Therefore, the volume in liters ([tex]\(V_{liters}\)[/tex]) is:
[tex]\[ V_{liters} = 48.08125 \, \text{m}^3 \times 1000 \, \text{liters/m}^3 = 48081.25 \, \text{liters} \][/tex]
### Summary
- The radius of the tank is [tex]\(1.75 \, \text{m}\)[/tex].
- The volume of the tank in cubic meters is [tex]\(48.08125 \, \text{m}^3\)[/tex].
- The volume of the tank in liters is [tex]\(48081.25 \, \text{liters}\)[/tex].
Thus, the calculated values are:
1. Radius of the tank: [tex]\(1.75 \, \text{m}\)[/tex]
2. Volume in cubic meters: [tex]\(48.08125 \, \text{m}^3\)[/tex]
3. Volume in liters: [tex]\(48081.25 \, \text{liters}\)[/tex]
