Question

The ratio of the circumference of a circle to the diameter of the circle is

• A. An integer
• B. A rational number
• C. An irrational number
• D. A whole number

Answer 1

The correct option is C

An irrational number

Compute the ratio :

Step 1: Circumference of the circle

Circumference of the circle is the measurement of the boundary of the circle.

The circumference (or) perimeter of a circle $=2\mathrm{\pi R}$

Where,

$R$ is the radius of the circle.

$\mathrm{\pi }$ is the mathematical constant with value of $3.14$.

Step 2: Compute the required ratio

Pi ($\mathrm{\pi }$) is a constant and it is the ratio of circumference to diameter of any circle.

Where, $C=\mathrm{\pi D}$

$C$ is the circumference of the circle.

$D$ is the diameter of the circle.

The ratio of circumference to diameter is $\frac{\mathrm{\pi }D}{D}$.

$\Rightarrow \mathrm{\pi }:1$

Thus, the ratio of circumference to diameter is $\mathrm{\pi }:1$ which is an irrational number.

Therefore, option (c) is the correct answer.

Step 3: Explanation for incorrect option

Option (a): An integer

Option (b): A Rational number

Option (d): A Whole number

Thus, the ratio of circumference to diameter is $\mathrm{\pi }:1$ which is an irrational number.

Therefore, option (a), (b) and (d) are incorrect answers.

Hence, option (c) is the correct answer.