The circumference of a circle and its diameter vary ____ with each other.

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Detailed Solution

The circumference of a circle and its diameter vary directly with each other.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
If two quantities are directly proportional, an increase in one will result in an increase in the other and a decrease in one will result in a decrease in the other.
We know that,
The circumference

P

of a circle of diameter

d

is given by:

P = π d

⇒ P d = π,

where

π

is a constant.
From the above equation, we can clearly see that the ratio of the circumference of a circle and its diameter is constant.
Therefore, the circumference of a circle and its diameter vary directly with each other.

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