Respuesta :
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 [tex]\times[/tex] radius and circumference = 2π [tex]\times[/tex] radius.
[tex]\text { Now, circumference }=\pi \times(2 \times \text { radius }) \rightarrow \text { circumference }=\pi \times \text { diameter }[/tex]
[tex]\text { At initial stage } \rightarrow \text { circumference }=9 \rightarrow \pi \times \text { diameter }=9 \rightarrow \text { diameter }=\frac{9}{\pi}[/tex]
[tex]\text { Now, after change } \rightarrow \text { circumference }=3 \rightarrow \pi \times \text { diameter }=3 \rightarrow \text { diameter }=\frac{3}{\pi}[/tex]
[tex]\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}[/tex]
Hence, the diameter decreases by a factor of 3.
Answer:
The circumference decreases by a factor of One-third.
Step-by-step explanation:
i just took he test
