Which statement is true about the circumference of a circle?
A. The circumference is equal to the radius of the circle.
B. The circumference is equal to the diameter of the circle.
C. The circumference is found by multiplying by the radius.
D. The circumference is found by multiplying by the diameter.
Answer (1)
The circumference of a circle is the distance around it.
The formula for the circumference using the diameter is C = π d .
The circumference is found by multiplying the diameter by π .
The true statement is: The circumference is found by multiplying by the diameter. $\boxed{The circumference is found by multiplying by the diameter.}
Explanation
Problem Analysis The question asks us to identify the true statement about the circumference of a circle. Let's analyze each option using our knowledge of circles.
Circumference Formulas The circumference of a circle is the distance around it. We have two formulas to calculate it:
Using the radius ( r ): C = 2 π r
Using the diameter ( d ): C = π d , where d = 2 r
Statement Evaluation Let's evaluate each statement:
Statement 1: The circumference is equal to the radius of the circle. This is incorrect because the circumference is 2 π times the radius.
Statement 2: The circumference is equal to the diameter of the circle. This is incorrect because the circumference is π times the diameter.
Statement 3: The circumference is found by multiplying by the radius. This is correct because C = 2 π r , so we multiply the radius by 2 π .
Statement 4: The circumference is found by multiplying by the diameter. This is also correct because C = π d , so we multiply the diameter by π .
Final Answer Since the question asks for only one true statement, and both statements 3 and 4 are correct, we need to choose the most accurate and complete one. Statement 4 is more direct and commonly used. Therefore, the most appropriate answer is:
The circumference is found by multiplying by the diameter.
Examples
Understanding the circumference of a circle is useful in many real-world situations. For example, if you're building a circular fence around a garden, you need to calculate the circumference to know how much fencing material to buy. Similarly, if you're designing a circular track, knowing the circumference helps determine the distance runners will cover in one lap. The relationship between a circle's diameter and circumference, C = π d , is fundamental in engineering, construction, and many other fields.
