Differentiating simple problems relating to area

[Mjr1991]

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?

Any help would be appreciated, I'm a bit rusty on calculus, cheers

 

[SammyS]

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

Hello Mjr1991. Welcome to PF !

What have you tried?

Where are you stuck?

Have you read the rules of this forum? -- particularly the part regarding homework Help.

 

[Mjr1991]

The second part has now been completed! However the second part I don't understand the whole concept of splitting it into two, all I am unsure of is how to start the question, the rest should be fine, many thanks if you can push me in the right direction

 

[SammyS]

Suppose we cut the rope in two, one piece has a length of ... let's call it L .

What's the length of the other piece?

If we form the piece of length L into a circle, what is the area of that circle. (You might first find it necessary to find the diameter & then the radius.)

What's the area of the square?