Step 1: Understanding the Question:
The question asks about the relationship between log taper (the rate at which a log's diameter decreases from the thick end to the thin end) and the recovery of sawn timber.
Step 2: Detailed Explanation:
• Commercial Utility: In sawmill operations, when a round log is converted into square or rectangular lumber, the "thin end" diameter acts as the limiting factor. Any material outside the cylinder defined by the thin-end diameter is lost as slabs or waste.
• Impact of Taper: If a log has a very high rate of taper (it narrows quickly), the difference between the thick end and thin end is large. To get a standard-sized beam without too much waste, the length of the log must be kept shorter. Longer logs with high taper result in excessive loss at the thick end.
• Statement A analysis: "The diameter at the thin end determines the sawn volume... greater taper, lesser is the length of the log." This is a fundamental principle of timber conversion. A smaller thin-end diameter limits the maximum width/thickness of boards, and high taper necessitates short logs to maximize recovery. This statement is correct.
• Statement D analysis: Suggests the thick end determines volume and greater taper allows greater length. This is incorrect because the thick end contains "slabbing" waste, and increasing length in high-taper logs increases waste exponentially.
Step 3: Final Answer:
Only Statement A is logically and technically correct in the context of log volume and taper.