Question

In a rectangular field which measures 15 m 8 m cows are tied with a rope of length 3 m at four corners of the field and also at the centre .find the area of the field where none of the cow can graze

Answer 1

Answer:

63.48 m²

Step-by-step explanation:

In a rectangular field which measures 15 m 8 m cows are tied with a rope of length 3 m at four corners of the field and also at the centre .find the area of the field where none of the cow can graze

Rectangle Are = 15 * 8 = 120 m²

Cows at corner Can graze for 90 deg angle of a circle

Each Cow At corner can Graze = (90/360)π * 3²= 9π/4  m²

4 Cosw at corner will graze = 4 * 9π/4  = 9π  m²

Cow at center will graze = π * 3² = 9π  m²

Total Area Grazes = 18π  m²

Lets check if Any area is covered by two cows

3 + 3 = 6 < 8 & 15

Diagonal = √8² + 15² = 17

3  + 6 + 3 = 12 < 17

So Not ANy area is covered by two cows

=

Area remained ungrazed = 120 -  18π  m²

Using π = 3.14    

Area remained ungrazed = 63.48 m²

Answer 2

Answer:

Area of Rectangular field not grazed is 63.48 m².

Step-by-step explanation:

Given:

Length of rectangle = 15 m

Width of the Rectangle = 8 m

Length of the rope = 3 m

Cow are tied at 4 corners and at center of the rectangular field.

To find: Area of Rectangular field not grazed.

Area of the field = length × width = 15 × 8 = 120 m²

We find Area of field grazed by cows using area of sector and area of circle formulas.

Area of Sector = $\frac{\theta}{360}\times\pi r^2$

Area of a circle = πr² = π × 3² = 9π = 9 × 3.14 = 28.26 m²

Area grazed at all corner are equal.

So, Total Area Grazed at corners = $4\times\frac{90}{360}\times\pi\times3^2$

                                                       $=4\times\frac{1}{4}\times3.14\times9$

                                                       $=28.26\:m^2$

So, Area left to Graze = 120 - ( 28.26 + 28.26 ) = 120 - 56.52 = 63.48 m²

Therefore, Area of Rectangular field not grazed is 63.48 m².