jmc

Question

The circular region of the sign (below, left) has an area of 154 square inches. Vanessa would like to place a tiny ribbon (shaded) around the circle's edge. To be sure she has enough ribbon, she decides to buy 2 inches more of the ribbon than the original circle's circumference. How many inches of ribbon will Vanessa need to buy if she estimates

π = \frac{22}{7}

?

Accepted Answer

Say the radius of the circle is r. Then the area of the circle is r^2, which we estimate to 154=227r^2. If we multiply both sides by 722, we get r^2=49 or r=7. The circle's circumference is 2 r, which we again estimate to 447r=44. Vanessa wants two extra inches of ribbon, so she needs to buy 44+2=46 inches of ribbon.