Solution: Let the radius of the ball be r, r=0.4m, the projection of the ball be an ellipse, and the minor axis b = r..

In the projection, od = OE = of = R.

Because △OAD is congruent △OAE

So ∠ oad = ∠ OAE = 30.

So OE/AE = tan 30

AE=√3r

Because △COE is congruent △COF

So ∠ family = ∠ COF = 30.

So CE/OE=? tan∠COE=tan30

CE=(√3/3)r

So 2a = ac = ae+ce = (4 √ 3/3) r.

a=(2√3/3)r

Projection area S=πab=π? (2√3/3)r？ r=(0.32π√3)/3