max / min questions (1 Viewer)

[Petinga]

Help needed for some max / min questions

1. A piece of wire of length 30cm is cut into 2 sections. Each section is then bent into the shape of a square. Find the smallest possible value of the sum of the areas of the two squares.

2. A closed box in the shape of a cuboid, the length of whose base is twice the width, has a total SA of 216 cm squared. If the width of the base is xcm, find:
a)the length of the base and height in terms of x
b)the volume of the box in terms of x
c) the maximum volume of the box


I need some solutions desperately

 

[Trev]

1)
Let lengths be x and y, so x + y = 30.
Therefore, one side length of a square is x/4 or y/4 so area of squares is x²/16 and y²/16.
∴ A = 1/16[x²+y²].
Sub x=30-y into A which gives A=1/16[900-60y+2y²]
dA/dy = 1/16[-60+4y]
When dA/dy=0, max/min points, ie. where y=15. (so, x=15 also).
So smallest sum of area's is A=1/16[15²+15²] = whatever.

 

[pLuvia]

1. A piece of wire of length 30cm is cut into 2 sections. Each section is then bent into the shape of a square. Find the smallest possible value of the sum of the areas of the two squares.

2. A closed box in the shape of a cuboid, the length of whose base is twice the width, has a total SA of 216 cm squared. If the width of the base is xcm, find:
a)the length of the base and height in terms of x
b)the volume of the box in terms of x
c) the maximum volume of the box


I need some solutions desperately

a)the length of the base and height in terms of x

i dun understand this question?

 

[acmilan]

a)the length of the base and height in terms of x

i dun understand this question?

Find the length of the base and height in terms of x?

 

[Petinga]

yes thats correct