The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
The correct answer is 8π.
To determine the circumference of the tree’s ring, we need to use the mathematical formula that relates a circle’s circumference to its diameter. The circumference is the distance around the outer edge of a circle, much like the perimeter of a square or rectangle. The diameter is the distance straight across the circle, passing through its center.
The formula for the circumference (C) of a circle is:
C = πd
In this formula, ‘d’ represents the diameter, and ‘π’ (pi) is a special mathematical constant, approximately equal to 3.14159. The problem provides the exact information needed to solve for the circumference.
Here is the step by step calculation:
- Identify the given value. The problem states that the diameter of the tree’s ring is 8 inches. So, d = 8 in.
- Apply the circumference formula. We substitute the given diameter into the formula C = πd.
- Calculate the result.
C = π * 8
By convention, the numerical coefficient is written before the constant π.
C = 8π inches.
This result, 8π, represents the exact circumference of the ring. The options provided in the dropdown menu include this value.
It is also helpful to understand why the other options are incorrect. The option 4π would be the result if one mistakenly used the radius (which is half the diameter, or 4 inches) but forgot that the full formula using radius is C = 2πr, not C = πr. The options 4²π (which is 16π) and 8²π (which is 64π) are incorrect because they use the formula for the area of a circle (A = πr²), not its circumference.
