A sector cut from a circular sheet has a central angle of 40°, and the total distance right round its edge is 34 cm. What is the radius of the circle, in cm? (Use π = 22/7.)

The edge of a sector is two straight radii plus the curved arc. The arc = $(40/360)\times 2\times (22/7)xr=44r/63$, so the perimeter = $2r+44r/63=170r/63$. Setting $170r/63=34$ gives $r=34\times 63/170=12.6$ cm. (Check: $2r=25.2$ cm and the arc = 8.8 cm, and 25.2 + 8.8 = 34.) The trap 17 = 34/2 counts only the two radii and leaves the arc out of the perimeter; 48.68 does the opposite, solving $44r/63=34$ as though the whole 34 cm were arc; 25.2 is the pair of straight edges, $2r$, reported instead of the single radius asked for.