Question

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

Answer 1

Answer:

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 $\times$ radius and circumference = 2π $\times$ radius.

$\text { Now, circumference }=\pi \times(2 \times \text { radius }) \rightarrow \text { circumference }=\pi \times \text { diameter }$

$\text { At initial stage } \rightarrow \text { circumference }=9 \rightarrow \pi \times \text { diameter }=9 \rightarrow \text { diameter }=\frac{9}{\pi}$

$\text { Now, after change } \rightarrow \text { circumference }=3 \rightarrow \pi \times \text { diameter }=3 \rightarrow \text { diameter }=\frac{3}{\pi}$

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

Hence, the diameter decreases by a factor of 3.

Answer 2

Answer:

The circumference decreases by a factor of One-third.

Step-by-step explanation:

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