Question

If the diameter of a circle changes from 8 cm to 4 cm, how will the circumference change? A) multiples by 1 2 B) multiplies by 2 C) increases by 6 D) decreases by 6

Answer 1

The diameter is halved so the circumference will also be halved

Answer is option A multiplied by 1/2.

Answer 2

A) Multiples by
`(1)/(2)`

Explanation:

Let
`C_1` be circumference of original circle and
`C_2` 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.

`\text{Circumference of circle}=2\pi r`, 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.

`r_1=(8)/(2)=4\\r_2=(4)/(2)=2`

`(C_2)/(C_1)=(2\pi*r_2)/(2\pi*r_1)`

`(C_2)/(C_1)=(2\pi*2)/(2\pi*4)`

`(C_2)/(C_1)=(4\pi)/(8\pi)`

`(C_2)/(C_1)=(1)/(2)`

`(C_2)/(C_1)* C_1=(1)/(2)* C_1`

`C_2=(1)/(2)* C_1`

Therefore, the circumference of the new circle will be the
`(1)/(2)` the circumference of original circle and option A is the correct choice.