Question

The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of the circles in inches?

Answer 1

A dilation by a scale factor of 6 will cause the radius to increase by a factor of 6. So $r_{new} = 6r$. If we plug this value of r into the formula for the circumference of a circle we get $C = 2\pi r_{new} = 2\pi *6r = 12\pi r$

So basically N = 12r. You haven't given me any original radius, so I can't give you a constant for N, but if you do have that original radius you can just plug that into 12r.

Based on your comment, N = 12 * 9 = 108 inches

Answer 2

The value of n is 12 .

What is scale factor?

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

According to the question

The circle will be dilated by a scale factor of 6 .

so,

New radius of the circle R = 6r

As is it dilated by a scale factor of 6

Now ,

The circumference of the new circles = 2πR  

                                                              = 2.6π

                                                              = $12\pi r$  -------------------- (1)

and given circumference of the new circles = nπ  ---------------------(2)

when we compare both n = 12

Hence, the value of n is 12 .

 

                                                             

To know more about scale factor here:

https://brainly.com/question/22312172

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