A question is followed by two statements. Determine the sufficiency of the data to answer the question:
**Question**: What is the total storage capacity (in $\text{m}^3$) of a cylindrical grain silo?
- **Statement I**: The curved surface area of the silo is $220\text{ m}^2$.
- **Statement II**: The internal diameter of the base of the silo is $7\text{ m}$.
Which of the following conclusions regarding data sufficiency is/are TRUE?
Options:
(A) Statement I alone is sufficient to answer the question.
(B) Statement II alone is sufficient to answer the question.
(C) Both Statement I and Statement II together are sufficient to answer the question.
(D) Neither statement alone is sufficient to answer the question.
Answer Key:
C, D
Step-by-Step Solution & Explanation
**Method 1: Algebraic Data Sufficiency Analysis**
Cylinder volume $V = \pi r^2 h$. Curved surface area $\text{CSA} = 2\pi r h$.
- From Statement I: $2\pi r h = 220\text{ m}^2$. Since $r$ and $h$ are not individually known, $V = (2\pi r h) \times \frac{r}{2}$ cannot be uniquely determined. Insufficient.
- From Statement II: $2r = 7\text{ m} \implies r = 3.5\text{ m}$. Height $h$ remains completely unknown. Insufficient.
- Combining both statements: $r = 3.5\text{ m}$, so $V = 220 \times \frac{3.5}{2} = 385\text{ m}^3$. Fully determined.
Therefore, both statements together are sufficient (C), and neither alone is sufficient (D).