Question

Generally, the relationship between the diameter (d) and girth (G) of tree is given the formula ______________.

• A. d = 3.182 G
• B. d = 0.3182 G
• C. G = 0.3182 d
• D. G = 3.182 d

Hint:

Always remember: $G = \pi d$ and $d = G/\pi$. Since $1/\pi$ is roughly $0.318$, it's a quick way to convert girth to diameter.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the mathematical relationship between diameter ($d$) and girth (circumference, $G$) of a tree, assuming its cross-section is a perfect circle.

Step 2: Key Formula or Approach:
1. The formula for the circumference ($G$) of a circle is \( G = \pi \times d \).
2. To find $d$, we rearrange the formula: \( d = \frac{G}{\pi} \).

Step 3: Detailed Explanation:

• We know that \( \pi \approx 3.14159 \).

• Thus, \( d = \frac{1}{3.14159} \times G \).

• Let's calculate the value of $1/\pi$:
\[ \frac{1}{3.14159} \approx 0.3183 \]

• Rounding to four decimal places, we get the constant $0.3182$ or $0.3183$.

• Therefore, the relationship is \( d = 0.3182 \times G \).

• Conversely, \( G = \pi \times d \approx 3.14 \times d \), which is not listed as $3.182$ exactly in option D. Thus, B is the most standard conversion used in mensuration.

Step 4: Final Answer:
The relationship is given by the formula d = 0.3182 G.