To determine the 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
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
- [tex]\( \pi \)[/tex] (Pi) is a constant approximately equal to 3.14
Let's follow the steps to find the volume of the tank.
1. Determine the height ([tex]\(h\)[/tex]):
Given, the height of the tank is [tex]\( 5 \, \text{m} \)[/tex].
2. Determine the diameter of the base ([tex]\(d\)[/tex]):
Given, the diameter of the tank is [tex]\( 3.5 \, \text{m} \)[/tex].
3. Calculate the radius ([tex]\(r\)[/tex]):
The radius is half of the diameter. Therefore:
[tex]\[
r = \frac{d}{2} = \frac{3.5 \, \text{m}}{2} = 1.75 \, \text{m}
\][/tex]
4. Substitute the values given into the volume formula:
[tex]\[
V = \pi r^2 h
\][/tex]
5. Substitute [tex]\(\pi = 3.14\)[/tex], [tex]\(r = 1.75 \, \text{m}\)[/tex], and [tex]\(h = 5 \, \text{m}\)[/tex]:
[tex]\[
V = 3.14 \times (1.75)^2 \times 5
\][/tex]
6. Calculate [tex]\((1.75)^2\)[/tex]:
[tex]\[
(1.75)^2 = 3.0625
\][/tex]
7. Continue with the volume calculation:
[tex]\[
V = 3.14 \times 3.0625 \times 5
\][/tex]
8. Multiply [tex]\( 3.14 \)[/tex] by [tex]\( 3.0625 \)[/tex]:
[tex]\[
3.14 \times 3.0625 = 9.62125
\][/tex]
9. Finally, multiply by the height [tex]\( 5 \, \text{m} \)[/tex]:
[tex]\[
V = 9.62125 \times 5 = 48.08125 \, \text{m}^3
\][/tex]
Hence, the volume of the water tank is [tex]\( 48.08125 \, \text{m}^3 \)[/tex].
