Given an elliptical ranch with dimensions 2*R units horizontally and 1 unit vertically, a goat is tied to the fence inside the ranch using a leash of length r units. The angle formed between the point of tying and the horizontal axis is θ. Determine the area of grass the goat can graze.Given :R- half of the horizontal dimension of the ellipseθ - the angle formed by the point of tying and the horizontal axis.r - length of the leashSome examples :R = 0.75 , r=0.25, θ=310Ans : 0.091

In a square field labeled ABCD, with each side measuring 30 meters, lush grass covers the ground, enclosed by iron wires. Four cows, Red, Black, White, and Brown, are tethered by ropes at the corners A, B, C, and D respectively of the square field. Each rope has a length of 14 meters. The cows are restricted to grazing only within the confines of the square field. (Use π = 22/7)Q 113.   What is the area (in sq. meter) of grass that the red cow can graze?a)  77b)  115.5c)  154d)  184

Find the area of elliptical segment “V” if the major radius of ellipse is 4 inches, minor radius of ellipse is 3 inches, dimensional X=2.36 inches, dimension Y=2.42 inches.

he number of animals in a certain ranch are as follows: Goats = 14, Sheep = 6, Cows = 8, Pigs = 17. What angle would represent the number of sheep if the above information was represented on a pie chart?

In a square field labeled ABCD, with each side measuring 30 meters, lush grass covers the ground, enclosed by iron wires. Four cows, Red, Black, White, and Brown, are tethered by ropes at the corners A, B, C, and D respectively of the square field. Each rope has a length of 14 meters. The cows are restricted to grazing only within the confines of the square field. (Use π = 22/7)Q 116.   If a 5th cow is tethered at the center of the square field and does not graze within the area of the four cows, what could be the maximum length (in integer meters) of the rope for the 5th cow? (Use √2 = 1.414)a)  5b)  6c)  7d)  8

Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 80 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?