Sure, let's find the volume of the cylinder step-by-step.
### Step 1: Understanding the given values
- Diameter of the cylinder: 28 meters.
- Height of the cylinder: [tex]\( 7 \frac{1}{2} \)[/tex] meters (which is equivalent to 7.5 meters when converted to a decimal).
- Value of π (pi) to be used: [tex]\( \frac{22}{7} \)[/tex].
### Step 2: Calculate the radius
The radius of a cylinder is half its diameter. So,
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{28}{2} = 14 \text{ meters} \][/tex]
### Step 3: Calculate the volume using the formula for the volume of a cylinder
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius, [tex]\( h \)[/tex] is the height, and [tex]\( \pi \)[/tex] is approximately [tex]\( \frac{22}{7} \)[/tex].
### Step 4: Plug in the values
- Radius ([tex]\( r \)[/tex]) = 14 meters.
- Height ([tex]\( h \)[/tex]) = 7.5 meters.
- [tex]\( \pi \)[/tex] = [tex]\( \frac{22}{7} \)[/tex].
So,
[tex]\[ V = \left(\frac{22}{7}\right) \times (14)^2 \times 7.5 \][/tex]
### Step 5: Conduct the multiplication
First, compute the squared radius:
[tex]\[ (14)^2 = 196 \][/tex]
So the volume calculation becomes:
[tex]\[ V = \left(\frac{22}{7}\right) \times 196 \times 7.5 \][/tex]
Next, multiply 196 by 7.5:
[tex]\[ 196 \times 7.5 = 1470 \][/tex]
Then multiply by [tex]\( \pi \)[/tex] value:
[tex]\[ V = \left(\frac{22}{7}\right) \times 1470 \][/tex]
[tex]\[ V = 22 \times 210 \][/tex] (since 1470 / 7 = 210)
[tex]\[ V = 4620 \text{ cubic meters} \][/tex]
### Conclusion
Hence, the volume of the cylinder is:
[tex]\[ 4620 \text{ cubic meters} \][/tex]
So the correct answer is:
[tex]\[ 4620 \text{ cubic meters} \][/tex]
