Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The volume of tree can be estimated using a trunk cylinder form with a forms factor.
Reason (R) : The form factor adjustments for the tree trunk actual shape (tapering) is compared to a perfect cylinder as tree trunk aren't perfect cylinder.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explation of (A)
• B. Both (A) and (R) are correct but (R) is NOT the correct explation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Tree Form Factor Formula: \[ f = \frac{\text{Actual Tree Volume } (V)}{\text{Basal Area } (S) \times \text{Height } (h)} \] Since trees taper toward the top, $f$ is always less than 1 (typically $0.4--0.6$).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question tests tree volume estimation principles using tree form factor adjustments in forest mensuration.

Step 2: Mathematical Formula for Tree Volume:

• Cylindrical Reference Volume ($V_c$): \[ V_c = S \times h \] where $S$ is the basal area at DBH ($S = \frac{\pi D^2}{4}$) and $h$ is total tree height.
• Actual Tree Volume ($V$): \[ V = S \times h \times f \] where $f$ is the dimensionless form factor ($f = \frac{V}{S \times h}$).

Step 3: Detailed Explation:

• Assertion (A) correctly states that actual tree volume is calculated by applying a form factor to a reference trunk cylinder volume.
• Tree stems are not true geometric cylinders; they taper continuously from base to tip (resembling a combition of neiloid, paraboloid, and cone frustums).
• The form factor ($f < 1.0$) mathematically adjusts the cylinder volume calculation to account for actual stem taper.
• Therefore, Reason (R) is correct and provides the direct mathematical justification for Assertion (A).

Step 4: Fil Answer:
Both (A) and (R) are correct, and (R) is the correct explation of (A). Hence, option (A) is correct.