The discussion revolves around optimizing the area enclosed by two pieces of a rope, one shaped into a square and the other into a circle, with a total length of 25 meters. Additionally, a related problem involves maximizing the cross-sectional area of an open trapezoidal channel.
The conversation is ongoing, with participants seeking clarification on the problems and exploring various interpretations. Some guidance has been offered regarding the need to define the lengths of the rope pieces and the areas associated with the shapes formed.
The original poster mentions feeling "rusty" on calculus, indicating a potential gap in foundational understanding that may affect their approach to the problems. There is also a reference to forum rules regarding homework help, suggesting an awareness of the need for collaborative learning.
Hello Mjr1991. Welcome to PF !Mjr1991 said:Homework Statement
1. a)
A rope 25m long is cut into two pieces. One piece is bent into the shape of a square, and the other into the shape of a circle. How should the rope be cut to maximise the total area enclosed by the pieces? And how should it be cut in order to minimise the total area enclosed by the two pieces?
1. b)
The cross-section of an open channel is a trapezium with base 13 metres and sloping sides each 11 metres long. Calculate the width across the open top so that the cross-sectional area of the channel is a maximum.
(The shape of the trapezium is that the 'open top' is wider than the base of 13m, with the sides 11m long sloping to this from the base)
Any help would be appreciated, I'm a bit rusty on calculus, cheers