Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the height of a circular cone? I. The area of that cone is equal to the area of a rectangle whose length is 33 cm. II. The area of the base of that cone is 154 sq. cm.

### Concept & Logic To find the height of a cone, we need some combination of its volume, radius, and slant height. $$Height = \sqrt{l^2 - r^2}$$ or derived from $Volume = \frac{1}{3} \pi r^2 h$. ### Step-by-Step Solution 1. Evaluate Statement I alone: It equates the "area of that cone" (which is ambiguous but implies either curved or total surface area) to the area of a rectangle. We only know the length of the rectangle ($33\text{ cm}$), not its width. Thus, the actual numerical area remains unknown. Not sufficient. 2. Evaluate Statement II alone: Gives the area of the base as $154\text{ sq. cm}$ ($\pi r^2 = 154$). This allows us to find the radius $r$. However, with no information on volume or slant height, we cannot find the vertical height $h$. Not sufficient. 3. Combine Statements I and II: We still do not know the width of the rectangle mentioned in Statement I. Therefore, we still have no concrete numerical value for the surface area of the cone. Without it, we cannot bridge the gap to find the height. ### Exam Strategy & Shortcut Whenever a statement introduces a new shape (like the rectangle here) but leaves one of its critical dimensions (width) completely undefined, that statement yields an unknown variable, making it useless for finding a final numerical answer. ### Common Pitfall A common mistake is assuming standard missing variables, such as assuming the rectangle might be a square, or confusing "area of the cone" with "volume". Always stick strictly to what is written. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question**.