Question

the dimensions of a rectangular field are 60 and 80 meters. four cows or tied at the four corners of the field with ropes of lengths 10, 12, 14 and 16 meters respectively .The area of the grass that cows could eat in square metres is?

need explanation​

Answer 1

Answer- The above question is from the chapter 'Area Related to Circles'.

Concept used: Area of quadrant of a circle = $\frac{1}{4}$ π r² where r = radius of quadrant.

Given question: The dimensions of a rectangular field are 60 and 80 metres. Four cows are tied at the four corners of the field with ropes of lengths 10, 12, 14 and 16 metres respectively .The area of the grass that cows could eat in square metres is ______ .

Solution: We know that each angle of a rectangle is 90°.

So, the four cows tied at the four corners will make four quadrants of different radii in which they can graze.

For cow 1,

r = 10 m

Area of grass that cow 1 can eat = $\frac{1}{4}$ π r²

                                                       = $\frac{1}{4}$ π × 10²

                                                       = 25 π m²

For cow 2,

r = 12 m

Area of grass that cow 2 can eat = $\frac{1}{4}$ π r²

                                                        = $\frac{1}{4}$ π × 12²

                                                        = 36 π m²

For cow 3,

r = 14 m

Area of grass that cow 1 can eat = $\frac{1}{4}$ π r²

                                                       = $\frac{1}{4}$ π × 14²

                                                       = 49 π m²

For cow 4,

r = 16 m

Area of grass that cow 1 can eat = $\frac{1}{4}$ π r²

                                                        = $\frac{1}{4}$ π × 16²

                                                        = 64 π m²

Total area of grass that can be eaten = 25 π m² + 36 π m² + 49 π m² + 64 π m²  = 174 π m² = 546.86 m²

Area of rectangular field = length × breadth = 60 × 80 = 4800 m²

Area which is left ungrazed = 4800 - 546.86 = 4,253.14 m²