The radius of a semicircle is extended by 6 inches. how does the measure of the semicircles arc length change?

Let x be the original radius. Given that a semicircle will have an arc length of half of a circumference and C=2pr, the arc length will be just pr.

Now the difference of arc is then going to be:

p (6+x) - px

p (6+x-x)

6p inches

So the arc will be 6p inches longer. Or if you wish to approximate ...

≈18.85 inches