Question

scientists studied the influence of nutrient removal on long - term forest productivity. four replications of four different treatments were conducted. one type of sample collected for analysis was fallen woody debris. the volume of the fallen wood was calculated using smalians equation for log volume: ( v=\frac{(b + s)}{2}l ), where ( b ) equals the cross - sectional area at the butt end, ( s ) equals the cross - sectional area at the small end, and ( l ) equals length. based on the information provided, which of the following samples of fallen wood would have the greatest log volume?

• ( b = 5, s = 5, l = 5 )
• ( b = 10, s = 10, l = 10 )
• ( b = 10, s = 10, l = 20 )
• ( b = 10, s = 5, l = 15 )

Explanation:

Step1: Recall the formula

The formula for log volume is \( V=\frac{(B + S)}{2}\times L \).

Step2: Calculate V for each option

• For \( B = 5, S = 5, L = 5 \):

\( V=\frac{(5 + 5)}{2}\times5=\frac{10}{2}\times5 = 5\times5 = 25 \)

• For \( B = 10, S = 10, L = 10 \):

\( V=\frac{(10 + 10)}{2}\times10=\frac{20}{2}\times10 = 10\times10 = 100 \)

• For \( B = 10, S = 10, L = 20 \):

\( V=\frac{(10 + 10)}{2}\times20=\frac{20}{2}\times20 = 10\times20 = 200 \)

• For \( B = 10, S = 5, L = 15 \):

\( V=\frac{(10 + 5)}{2}\times15=\frac{15}{2}\times15 = 7.5\times15 = 112.5 \)

Comparing the volumes 25, 100, 200, and 112.5, we see that 200 is the largest, which corresponds to the option \( B = 10, S = 10, L = 20 \).

Answer:

B=10, S=10, L=20