Question

The ratio of the circumference of a circle to twice the diameter of the circle is
A. $\dfrac{{\text{$\pi$ }}}{{\text{4}}}$
B. $\dfrac{{\text{$\pi$ }}}{{\text{2}}}$
C. ${\text{$\pi$ }}$
D. ${\text{2$\pi$ }}$
E. ${\text{4$\pi$ }}$

Answer 1

Hint: We know equations to find the circumference and the diameter Circumference of a circle is given by ${\text{C = 2$\pi$ r}}$ and diameter of a circle is given by ${\text{D = 2r}}$. So, we find the circumference of the diameter. To get the required ratio we divide the circumference with two times the diameter.

Complete step by step answer:

For a circle, its circumference and diameter are functions of its radius.
Circumference of a circle is given by ${\text{C = 2$\pi$ r}}$
Diameter of a circle is given by ${\text{D = 2r}}$
We are asked to find the ratio of circumference to twice the diameter of the circle.
So, the required ratio can be found by,
${\text{Ratio = }}\dfrac{{\text{C}}}{{{\text{2D}}}}{\text{ = }}\dfrac{{{\text{2$\pi$ r}}}}{{{\text{2 $\times$ 2r}}}}$
After cancelling the common terms, we get,
${\text{Ratio = }}\dfrac{{\text{$\pi$ }}}{{\text{2}}}$
Therefore, the required ratio is $\dfrac{{\text{$\pi$ }}}{{\text{2}}}$.
So, the correct answer is option B.

Note: In order to find the ratio, we must divide the quantities in the given order. Otherwise the ratio we get will be the reciprocal of the required ratio. The formulas to find the circumference and diameter using radius must be known. We must take extra care while cancelling out the terms to get the final ratio. A circle can be defined as the collection of all the points that are equidistant from a given point. This given point is called the centre and the distance is called the radius. The diameter is the line connecting two points on a circle and passes through the centre. The length of the diameter is twice the radius. The circumference is the perimeter of the circle. Circles with the same radius have the same circumference.