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Q.

State whether the following statement is true or false.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, $= c d$ ⋅ If c or d is irrational, then $π$ is irrational.

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a

True

b

False

answer is A.

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Detailed Solution

Irrational numbers:
The numbers which cannot be expressed in the form

p q

, where p & q both are integers and q≠0 are called irrational numbers.
We know that Circumference = π × diameter
c = πd
π =

c d

π is the ratio of the circumference of a circle to the length of the diameter.
When we measure the length with the scale or any other device, we only get an approximate rational value so we may not realize that in c & d which one is irrational.
So, either c or d is irrational and hence,

c d

is irrational i.e π is irrational.
Hence, the given statement is true.
Therefore, the correct option is 1.

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