Answer :
Final answer:
The assertion that the circumference of a circle is 176 cm is true based on the reason that the circumference of a circle is equal to 2πr.So, the statement is true.
Explanation:
The student asks whether the assertion that the circumference of a circle is 176 cm is correct based on the reason that the circumference of a circle is equal to 2πr, which is a mathematical formula to calculate the circumference of a circle. To evaluate this, we first must understand the relationship between the circumference (C) and the radius (r) of a circle.
The ancient Greeks already determined that the circumference of a circle can be calculated using the formula C = 2πr, where π is the constant approximately equal to 3.14159. Therefore, if we have the circumference, we can find the radius by rearranging the formula to r = C / (2π). For a circumference of 176 cm, we have r = 176 cm / (2π) ≈ 28 cm. Since this process uses the correct formula for calculating the circumference of a circle based on its radius, the reason given is valid.
As a result, the assertion is logically consistent with the reason provided, assuming the algebraic manipulation has been done correctly. Therefore, the correct option in response to the student's question is True.
