Question

If the circumference of a circle is changed from 9 cm to 3 cm, how will the diameter change?

increases by a factor of 3
decreases by a factor of
increases by a factor of 4
decreases by a factor of 4

Answer 1

The circumference decreases by a factor of One-third.

Explanation:

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Answer 2

If the circumference of a circle is changed from 9 cm to 3 cm, then the diameter decreases by a factor of 3.

Solution:

Given, the circumference of a circle is changed from 9 cm to 3 cm,

We have to find how will the diameter change from the given equations?

We know that, diameter = 2
`*` radius and circumference = 2π
`*` radius.

`\text { Now, circumference }=\pi *(2 * \text { radius }) \rightarrow \text { circumference }=\pi * \text { diameter }`

`\text { At initial stage } \rightarrow \text { circumference }=9 \rightarrow \pi * \text { diameter }=9 \rightarrow \text { diameter }=(9)/(\pi)`

`\text { Now, after change } \rightarrow \text { circumference }=3 \rightarrow \pi * \text { diameter }=3 \rightarrow \text { diameter }=(3)/(\pi)`

`\text { Now, for finding change in factor }=\frac{\text { new diameter }}{\text { old diameter }}=((3)/(\pi))/((9)/(\pi))=(3)/(9)=(1)/(3)`

Hence, the diameter decreases by a factor of 3.