Answer:
A) Multiples by [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Let [tex]C_1[/tex] be circumference of original circle and [tex]C_2[/tex] be the circumference of new circle.
We have been given that the diameter of a circle changes from 8 cm to 4 cm. We are asked to find how the circumference of the circle will change.
We will use circumference of circle formula to solve our given problem.
[tex]\text{Circumference of circle}=2\pi r[/tex], where, r represents radius of the circle.
Since the radius of a circle is half the diameter, so we will divide the diameter of circle by 2 to get the radius.
[tex]r_1=\frac{8}{2}=4\\r_2=\frac{4}{2}=2[/tex]
[tex]\frac{C_2}{C_1}=\frac{2\pi*r_2}{2\pi*r_1}[/tex]
[tex]\frac{C_2}{C_1}=\frac{2\pi*2}{2\pi*4}[/tex]
[tex]\frac{C_2}{C_1}=\frac{4\pi}{8\pi}[/tex]
[tex]\frac{C_2}{C_1}=\frac{1}{2}[/tex]
[tex]\frac{C_2}{C_1}\times C_1=\frac{1}{2}\times C_1[/tex]
[tex]C_2=\frac{1}{2}\times C_1[/tex]
Therefore, the circumference of the new circle will be the [tex]\frac{1}{2}[/tex] the circumference of original circle and option A is the correct choice.
