To find the volume of the cylinder, we need to follow these steps:
1. Identify the given parameters:
- Diameter of the cylinder, [tex]\( d = 28 \)[/tex] meters
- Height of the cylinder, [tex]\( h = 9 \frac{1}{2} \)[/tex] meters
- Approximation for [tex]\(\pi\)[/tex], [tex]\(\pi = \frac{22}{7}\)[/tex]
2. Convert the diameter to the radius:
The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{28}{2} = 14 \text{ meters}
\][/tex]
3. Convert the height to a single number:
The height is given as a mixed number:
[tex]\[
h = 9 \frac{1}{2} = 9 + \frac{1}{2} = 9.5 \text{ meters}
\][/tex]
4. Use the formula for the volume of a cylinder:
The formula for the volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[
V = \pi r^2 h
\][/tex]
Substitute the given values into the formula.
[tex]\[
V = \left(\frac{22}{7}\right) \times (14)^2 \times 9.5
\][/tex]
5. Calculate the volume:
Perform the calculations step-by-step:
- First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = 14^2 = 196
\][/tex]
- Then, multiply by the height:
[tex]\[
196 \times 9.5 = 1862
\][/tex]
- Finally, multiply by [tex]\(\frac{22}{7}\)[/tex]:
[tex]\[
V = \left(\frac{22}{7}\right) \times 1862 = 5852 \text{ cubic meters}
\][/tex]
So, the volume of the cylinder is [tex]\( 5852 \)[/tex] cubic meters.
The correct answer is not among the options provided, but the closest understanding would be to acknowledge that our volume calculation based on the provided dimensions and approximations results in 5852 cubic meters.
