A horse is tied with a rope of
length 7meter at one corner of a square field
having a side of 10 meter . the area of the field
out of reach for the horse is ?
Did you make a sketch?
Shade in the area not reached by the horse
The area reached by the horse is 1/4 of a circle with radius of 7 m
that area = (1/4)π(49) = 12.25π m^2
Area of the whole square = 100 m^2
So .....
To find the area of the field that is out of reach for the horse, we need to determine the area of the square field and subtract the area of the circle that the horse can reach.
First, let's calculate the area of the square field. The formula for the area of a square is side length squared. In this case, the side length of the square is 10 meters, so the area is:
Area of the square field = side length × side length = 10m × 10m = 100 square meters.
Next, let's find the area of the circle that the horse can reach. The area of a circle is given by the formula pi × radius squared. In this case, the length of the rope tied to the horse acts as the radius of the circle since it represents the maximum distance the horse can reach. The length of the rope is 7 meters, so the radius is 7 meters.
Area of the circle = π × (radius)^2 = π × (7m)^2.
Now, we can calculate the area of the circle. However, the value of π is an irrational number, so typically, we use an approximation such as 3.14.
Area of the circle = 3.14 × (7m)^2.
To calculate this, we'll do the following steps:
1) 7m × 7m = 49 square meters
2) 3.14 × 49 square meters ≈ 153.86 square meters.
Now, we have the area of the circle, which is approximately 153.86 square meters.
Finally, to find the area of the field that is out of reach for the horse, we subtract the area of the circle from the area of the square:
Area out of reach = Area of square field - Area of circle
= 100 square meters - 153.86 square meters.
Since the area of the circle is larger than the area of the square field, the result will be negative. This indicates that the entire field is within the reach of the horse, and there is no area out of reach.