“Circumference of a circle is twice the radius” a) True b) False
The Correct Answer and Explanation is :
The statement “Circumference of a circle is twice the radius” is False.
Explanation:
To understand why this statement is false, we need to review the formula for the circumference of a circle in terms of its radius.
Formula for Circumference:
The circumference ( C ) of a circle is the distance around the edge of the circle, and it is given by the formula:
[
C = 2 \pi r
]
where:
- ( C ) is the circumference,
- ( \pi ) (pi) is a mathematical constant approximately equal to 3.14159,
- ( r ) is the radius of the circle.
According to this formula, the circumference of a circle is twice the product of ( \pi ) and the radius. Thus, rather than being simply “twice the radius,” the circumference is twice the radius multiplied by ( \pi ).
Why the Statement is False:
The radius (( r )) is the distance from the center of the circle to any point on its edge. If the circumference were simply twice the radius, the formula would look like ( C = 2r ). However, this would omit the important factor of ( \pi ), which accounts for the circular shape of the circumference.
In other words:
- If a circle has a radius of 1 unit, then its circumference would be ( 2 \pi \approx 6.28 ) units, not 2 units.
- The circumference is always larger than twice the radius by a factor of ( \pi ).
Correct Interpretation:
The circumference of a circle is approximately 6.28 times the radius because ( 2 \pi \approx 6.28 ). This reflects the actual relationship between a circle’s circumference and its radius, making the given statement incorrect.
In summary, the correct answer to the question is “False,” because the circumference of a circle is not merely twice the radius but rather ( 2 \pi ) times the radius.