Question

Quadrilateral ABDE is a rectangle. DE = 4 in. and BD = 6 in.

If the rectangle is rotated about a line through CF, cylinder Y is created. If the rectangle is rotated about a line through GH, cylinder Z is created.

Rectangle A B D E is shown. Point C is the midpoint of side D B, point G is the midpoint of side B A, point F is the midpoint of side E A, and point H is the midpoint of side D E. Side D E has a length of 4 inches and side B D has a length of 6 inches.

What is the difference in the measures of the radii of cylinder Y and cylinder Z, in inches?

1
2
4
5

Answer 1

Place the rectangle with D = (0,0), E = (4,0), B = (0,6), A = (4,6).
C = midpoint of DB = (0,3) and F = midpoint of EA = (4,3), so CF is the horizontal midline y = 3; rotating about CF gives radius = distance to top (or bottom) = 6/2 = 3 in.
G = midpoint of BA = (2,6) and H = midpoint of DE = (2,0), so GH is the vertical midline x = 2; rotating about GH gives radius = distance to left (or right) = 4/2 = 2 in.

Difference = 3 − 2 = 1 inch. Answer: 1.