Question

A channel is to be constructed out of a sheet of metal, to allow gravel to be removed from a mining site. The sheet of metal has a width of 40cm and each side is bent up (at the same angle of 45 degrees from the horizontal) so as to maximise the amount of gravel that the channel can carry.

Determine the portion w of the metal sheet to be bent up on each side, and also calculate the maximum cross sectional area of the channel.

Answer 1

So i think you have to find an equation for the cross sectional area and differentiate it to find the maximum, however i cant do it. If anyone could help me out i would appreciate it.

Answer 2

The diagonals are 40 cm each, correct ?

Answer 3

yes i believe so

Answer 4

and what is the portion w ?

Answer 5

thats what we are trying to figure out

Answer 6

I mean, which part of the pic is the portion w ?

Answer 7

w is the length of the bent up sides

Answer 8

I got to go, I always leave at 10:30 pm, sorry -:(

Maybe, @iambatman can finish it off ?

Answer 9

I am in eastern Zone, in US.

Answer 10

thanks anyway

Answer 11

Have a good night/morning !