Question

If the radius of the circle is doubled, by what number is the circumference multiplied?

Answer 1

Circumference is also doubled (multiplied by 2)

Answer 2

Answer:

The number by which the circumference is multiplied is:

                               2

Step-by-step explanation:

We know that the circumference of the circle in terms of the radius r is given by:

        $\text{Circumference}=2\pi r$

Now, if the radius is doubled.

i.e.

$r'=2r$

Hence, the circumference of the new circle is given by:

$\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)$

i.e.

$\text{Circumference of new circle}=2\times \text{Circumference of original circle}$

The constant by which the circumference is multiplied is: 2