Question

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

Answer 1

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