Let's solve the problem of determining how much grain can be held in a cylindrical silo using the given value for [tex]\(\pi\)[/tex] and typical dimensions for such a silo.
1. Identify the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
where:
- [tex]\(V\)[/tex] is the volume,
- [tex]\(r\)[/tex] is the radius of the base,
- [tex]\(h\)[/tex] is the height of the cylinder.
2. Given typical dimensions:
- Radius ([tex]\(r\)[/tex]) = 10 feet
- Height ([tex]\(h\)[/tex]) = 100 feet
3. Calculate the volume using the provided value for [tex]\(\pi = 3.14\)[/tex]:
[tex]\[
V = 3.14 \times (10)^2 \times 100
\][/tex]
[tex]\[
V = 3.14 \times 100 \times 100
\][/tex]
[tex]\[
V = 3.14 \times 10000
\][/tex]
[tex]\[
V = 31400 \text{ cubic feet}
\][/tex]
4. Compare this calculated volume with the provided answer choices:
- A. [tex]\(28048.2\)[/tex] cubic feet
- B. [tex]\(29858.5\)[/tex] cubic feet
- C. [tex]\(23220.5\)[/tex] cubic feet
- D. [tex]\(26225.3\)[/tex] cubic feet
5. Determine the correct answer:
The volume we calculated is [tex]\(31400\)[/tex] cubic feet. None of the given options match this volume exactly. Therefore, without knowing further context such as potential error margin or rounding practices, but acknowledging the calculated typical volume for a cylindrical silo:
The closest answer is not provided, but our calculation lands exactly at [tex]\(31400\)[/tex] cubic feet.
If a different radius or height were specified, these answers might make sense, but given our dimensions and the closest scrutiny, none of the options directly align, indicating a discrepancy between practical silo measures or rounding specifics.
In conclusion, the farmer's silo can hold [tex]\(31400\)[/tex] cubic feet of grain.
