Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 m².

Given,

Grazed area = 9856 m²

Radius of circular field = Length of the rope

A cow tethered to a fixed point by a rope will graze in a circular pattern.

Area of circle = πr²

⇒ 9856 = $\dfrac{22}{7}$ × r²

⇒ r² = $\dfrac{9856 × 7}{22}$

⇒ r² = $\dfrac{68992}{22}$

⇒ r² = 3136

⇒ r = $\sqrt{3136}$ = 56 m.

Hence, length of the rope = 56 m.