You are a farmer, with a round fenced field of radius 10 meters. You tie your goat to the fence with a rope, and realize that the goat can eat exactly half of the field. How long is the rope?
11.587 m
R = 1.1587*10=11.587 m solution is here: http://mathforum.org/dr.math/faq/faq.grazing.html
A teacher has a rope with length equal to L cm. Using the entire rope, he forms the edges of a non-square rectangle with area equal to A cm2. What is the length of the smaller side of this rectangle, in cm ? (In terms of L and A)
A circular sector can be folded into a cone by joining its two radii. For a circular sector with a radius equal to 1, what is the maximum volume of the cone? If the circular sector has a central angle θ, what is the value of θ at the maximum volume?
There are four sticks of length ‘a’ and four more sticks of length ‘b’. The length of ‘b’ is exactly half of the length of ‘a’. The task is to make three equal squares using the given 8 sticks.
The altitude of a circular cylinder is increased 12 times and the base area is decreased to one ninth of its value. How much would be the change in surface area of new cylinder?
