To calculate the capacity (volume) of a cylindrical water tank, we can use the formula for the volume of a cylinder, which is given by [tex]\( V = \pi r^2 h \)[/tex], where:
- [tex]\( V \)[/tex] is the volume of the cylinder,
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14,
- [tex]\( r \)[/tex] is the radius of the base of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder.
Let's go through the steps:
1. Height of the tank (h):
The height of the tank is given as [tex]\( 5 \, \text{m} \)[/tex].
2. Diameter of the tank:
The diameter of the tank is given as [tex]\( 3.5 \, \text{m} \)[/tex].
3. Radius of the tank (r):
The radius is half the diameter. Therefore,
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{3.5 \, \text{m}}{2} = 1.75 \, \text{m}
\][/tex]
4. Constant [tex]\(\pi\)[/tex]:
According to the problem, [tex]\(\pi\)[/tex] is given as [tex]\( 3.14 \)[/tex].
5. Calculate the volume (V):
Using the formula [tex]\( V = \pi r^2 h \)[/tex],
[tex]\[
V = 3.14 \times (1.75 \, \text{m})^2 \times 5 \, \text{m}
\][/tex]
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = (1.75)^2 = 3.0625 \, \text{m}^2
\][/tex]
Now, calculate [tex]\( \pi r^2 \)[/tex]:
[tex]\[
\pi r^2 = 3.14 \times 3.0625 = 9.61375
\][/tex]
Finally, calculate the volume:
[tex]\[
V = 9.61375 \times 5 = 48.08125 \, \text{m}^3
\][/tex]
Therefore, the capacity (volume) of the water tank is [tex]\( 48.08125 \, \text{m}^3 \)[/tex].
