Question

A student solved for the radius of a circle with a circumference of 12π. In which step did the student make an error?

Answer 1

The student make an error in step 4.

Explanation:

Given : A student solved for the radius of a circle with a circumference of 12π.

To find : In which step did the student make an error?

Solution :

Let us write each step to find the radius of a circle from its circumference

Step 1 - Circumference of circle,

`C=2\pi r`

Step 2 - Substitute the given circumference,

`12\pi= 2\pi r`

Step 3 - Divide both sides by 2π,

`(12\pi )/(2\pi )=(2\pi r)/(2\pi )`

Step 4 - Solve

`6=\pi r` , it is incorrect as π get cancelled

Correct step is
`6=r`

The radius of the circle is 6 cm.

Step 5 -
`(6)/(\pi )=(\pi r)/(\pi)`

Step 6 -
`(6)/(\pi )=r`

The student made a mistake in step 4 so step 5 and 6 is automatically invalid.

Therefore, the student make an error in step 4.