Question

The length of a sido of a square fiold is 20 m. A cow is tied at the corner by means of a 6 m long rope. Find the area of the field which the cow can graze. Also fwd the increase in the grazing area, if length of the rope is increased by 2 m.(???? = 3.14)

Answer 1

Area of circular arc(t) = $0.5\beta a^{2}$

where a is radius = 6 m and $\beta = \pi /2$

hence, t = 28.275 $m^{2}$

Now, rope lenght increase by 2 m

hence,new radius = 8 m

so,new area(s) = 50.265$m^{2}$

So, increase in the grading area = s-t = $22m^{2}$

Answer 2

length of side of square field = 20m
cow is tied at the corner by means of a 6m long rope. e.g., Length of rope = 6m

length of rope = radius of circular part , where cow can graze , r = 6m

at corner of square , angle = 90°
so, area of field where cow can graze = 1/4 × area of circle
= 1/4 × πr²
= 1/4 × 3.14 × (6)²
= 1/4 × 3.14 × 36
= 9 × 3.14 = 28.26 m²

now, if rope is increased by 2m
then, radius of circular part where cow can graze , r' = 6 + 2 = 8m
now, area of field where cow can graze = 1/4 πr'²
= 1/4 × 3.14 × (8)²
= 1/4 × 3.14 × 64
= 16 × 3.14 = 50.24 m²

now, increase in the grazing area = 50.24 - 28.26 = 21.98m²