Here the increase in the length of the rope simply means that there is increase in the radius of the circle within which cow can graze. Now to find the additional area available for grazing can be easily be found by simply subtracting the initial area available for grazing from the new area available.

Initial radius = r = 16 cm

Increased radius = R = 23 cm

Additional ground available = Area of new ground – Initial area → eqn1

Initial area of ground = π(r²)

⇒ Initial area of ground = π(16²)

⇒ Initial area of ground = 256π → eqn2

Area of new ground = πR²

⇒ Area of new ground = π(23²)

⇒ Area of new ground = 529π → eqn3

Now put the values of equation 2 and 3 in equation 1

⇒ Additional area of ground available = 529π – 256π

⇒ Additional area available = (529 – 256)π (Taking π common)

⇒ Additional ground available = 273π

(22×273)/7

= 6006/7

= 858 cm²

The additional ground available is 858 cm².