Question

What is the height of a circular cone? 
Statement I - The area of that cone is equal to the area of a rectangle whose length is 33 cm. 
Statement II - The area of the base of that cone is 154 sq. cm.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both, statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

When solving geometry problems, use relationships between surface area, volume, and dimensions to find missing values.

Answer 1

The Correct Option is C

From Statement I:
The area of the cone is equal to the area of a rectangle with a length of 33 cm. This gives us information about the surface area, but we still do not know enough to calculate the height of the cone.
From Statement II:
The area of the base of the cone is 154 sq. cm. This gives us the radius of the cone’s base using the formula \( {Area} = \pi r^2 \), but we still don’t know the slant height or the full height of the cone.
Combining both statements: From Statement II, we can calculate the radius of the base. From Statement I, we can find the slant height of the cone (since the area of the rectangle involves the slant height and circumference).
Using these values, we can find the height of the cone using the Pythagorean theorem. Thus, both statements are needed to answer the question.