If a cow is tied to a silo with radius r by a rope just long enough to reach the opposite side, what is the a?

area available for grazing?

Area=Pir^2=3.1416 x r^2

Area of a circle (pi*r^2)

Since the cow is ties to a rope which is stuck at one end, the cow will be able to move with the rope in a circular manner. This is the maximum area that the cow can cover. Area of a circle is pi * r^2 Since the length of the rope is 'r' and this is the distance between the cow and the centre of the circle (the fixed point), the radius of this circle is also 'r'. Therefore, the area that the cow can cover is pi * r^2 = 3.14 * r^2

let R be the length of the rope . with respect to r, if the cow was able to reach the opposite side of the silo .... then the length of the rope is half the circumference of the silo . thus length of rope = πr = R half the portion of the region (the one opposite the silo) is a semicircle. the area is πR^2/2 = π^3 r^2/2 the other half portion is an ellipse where one dimension is πr and the other dimension is 2r. note: the area of an ellipse is πab thus the area of the half-ellipse is π(πr)(2r)/2 = π^2 r^2 thus the total area is π^2 r^2 + π^3 r^2/2 - πr^2 .