a cow tied with a rope of 7 m on the corner of a square field 11 cm long is grazing the find the area of the grazed field by the cow
Answers
Answer:
278.5 m².
Step-by-step explanation:
The required area=area of the square field-area of the sector with radius r=21m and
θ=90∘
=⎝⎜⎜⎛25×25−360722×21×21×90⎠⎟⎟⎞m2
=(625−422×3×21)m2
=(625−346.5)m2
=278.5 m2
A cow is tied with a rope of length 7 m at a corner of a rectangular field
All angles of rectangle are 90°
Length of rope = 7 m
Area of sector that cow can graze =\frac{\theta}{360} \pi r^2 = \frac{90}{360} \times \frac{22}{7} 7^2 =38.5 m^2
360
θ
πr
2
=
360
90
×
7
22
7
2
=38.5m
2
Length of rectangular field = 20 m
Breadth of rectangular field = 16 m
Area of field =Length \times Breadth = 20 \times 16 = 320 m^2Length×Breadth=20×16=320m
2
The area of the field in which the cow cannot graze = 320 - 38.5 = 281.5 m^2320−38.5=281.5m
2
Hence The area of the field in which the cow cannot graze is 281.5 m^2