Question

Two flat, circular plates are placed on a circular table top. The diameter of each plate is equal to the radius of the table top. Approximately how many square feet of the tabletop or not covered by the plates? Show or explain your work. Use 3.14 for pi

Answer 1

r of plate = r
2 r = R tabletop
area covered = 2 * pi r^2
total area of table = pi R^2 = pi (2r)^2 = 4 pi r^2
so area not covered = 2 pi r^2

Answer 2

r = Radius of the table.
r/2 = Radius of each plate.

At = pi * r^2. = Area of table top.
Ap = 2 * (pi * (r/2)^2) = 2 * (pi * r^2/4) = pi*r^2/2. = Area of 2 plates.

A = At - Ap = pi*r^2 - pi*r^2/2 = pi*r^2/2 = Area not covered.
So 1/2 of the area is not covered.