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 (2)
The circumference C of a circle relates to its radius r by the formula C = 2 π r .
The diameter d of a circle is twice its radius: d = 2 r , so C = π d .
The circumference is found by multiplying the radius by 2 π or the diameter by π .
Therefore, the circumference is found by multiplying by the radius and the circumference is found by multiplying by the diameter.
Explanation
Problem Analysis The question asks us to identify the correct statement about the circumference of a circle. Let's analyze the relationship between a circle's circumference, radius, and diameter.
Formulas for Circumference and Diameter The circumference of a circle is the distance around it. The formula for the circumference C of a circle in terms of its radius r is: C = 2 π r where π (pi) is a mathematical constant approximately equal to 3.14159.
The diameter d of a circle is the distance across the circle through its center. The diameter is twice the radius: d = 2 r We can express the circumference in terms of the diameter by substituting d = 2 r into the circumference formula: C = π d
Evaluating the Statements Now, let's evaluate each statement:
The circumference is equal to the radius of the circle. This statement is false. The circumference is 2 π times the radius, not equal to the radius.
The circumference is equal to the diameter of the circle. This statement is false. The circumference is π times the diameter, not equal to the diameter.
The circumference is found by multiplying by the radius. This statement is true. The formula C = 2 π r shows that the circumference is found by multiplying the radius r by 2 π .
The circumference is found by multiplying by the diameter. This statement is also true. The formula C = π d shows that the circumference is found by multiplying the diameter d by π .
Conclusion Both statements 3 and 4 are correct. The circumference can be found by multiplying the radius by 2 π or by multiplying the diameter by π .
Examples
Understanding the circumference of a circle is crucial in many real-world applications. For instance, when designing a circular garden, knowing the circumference helps determine the amount of fencing needed. Similarly, in engineering, calculating the circumference of a wheel is essential for determining how far a vehicle travels in one revolution. These calculations ensure accuracy and efficiency in various projects, from small-scale designs to large-scale constructions.
The true statements about the circumference of a circle are that it is found by multiplying the radius by 2 θ (Statement C) and by multiplying the diameter by θ (Statement D). Therefore, both C and D are correct. The circumference is not equal to either the radius or diameter.
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