Question

The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. What is the volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelepiped on a square base?

Answer 1

Correct Answer: 2

Concept:

• Largest square inside circle → diagonal = diameter
• Volume = base area $\times$ height

Step 1: Find square side.
\[ \text{Radius} = 1.5 \Rightarrow \text{Diameter} = 3 \] For square: \[ \text{Diagonal} = 3 \Rightarrow \text{Side} = \frac{3}{\sqrt{2}} \]
Step 2: Base area.
\[ \left(\frac{3}{\sqrt{2}}\right)^2 = \frac{9}{2} \]
Step 3: Volume.
\[ \text{Volume} = \frac{9}{2} \times 10 = 45 \text{ m}^3 \]
Step 4: Option analysis.

• (A) Incorrect $\times$
• (B) Correct \checkmark
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).