A goat is tethered with a 30-m rope to a fixed point on a silo with a 20-m radius. What is the area around the silo on which the goat can eat grass?
What you will have to do is find the areas of both circles and subract them to get the final answer. If the silo is has a 20m radius, then you must apply the formula for the area of the circle, which is pi r ^2 Then plug in the values: pi(20)^2 The area of the silo is 400pi. Now take the area of the circle with the goat. Remember, the goat can go anywhere around the fixed piont, which is a circle. The 30m rope is the radius of the circle. Therefore, you will have: pi(30)^2= 900pi Now subract the two values: 900pi - 400pi= 500pi. That's how much area the goat can eat around the silo. If they want pi calculated, just multiply 500 times 3.14 to get the exact answer. Hope this helps.
Wow...classic math problem!!! I seem to get the answer of 45. which is the result of evaluating twice the integral (from 0 to 3/2) of the expression (30-20x) with respect to x. haha..if wrong, lemme know, back to the drawing board. Take Two: The solution requires the partial integration of the area inside the INVOLUTE created by the stretched rope around the circular silo. Unfortunately, I got stumped by that INVOLUTE thing. I was able to make a diagram of the problem - shouldn't that count as half-correct?? lol You got me chasing my integral calculus, algebra, geometry and now kinematics trying to solve this problem...lol...this is so classic...circa 1960(?). I surrender!
