Finding Possible Width Range for a Rectangular Solid with a Given Volume

[zeion]

Homework Statement

A rectangle solid is to be constructed with a special kind of wire along all the edges. The length of the base is to be twice the width of the base. The height of the rectangular solid is such that the total amount of wire used (for the whole figure) is 40cm. Find the range of possible values for the width of the base so that the volume of the figure will lie between 2 cm^3 and 4 cm^3.

Homework Equations

The Attempt at a Solution

I define the base width as x, then the length is 2x, height as y, then I write the height in terms of x I have the equation: 4x + 8x + 4y = 40. So y = 10-3x.

Now I solve one side of the inequality

x(2x)(10-3x) = 4

and end up with 10x^2 - 3x^3 - 2 = 0

And can't find any whole roots.

 

[Mark44]

Homework Statement

A rectangle solid is to be constructed with a special kind of wire along all the edges. The length of the base is to be twice the width of the base. The height of the rectangular solid is such that the total amount of wire used (for the whole figure) is 40cm. Find the range of possible values for the width of the base so that the volume of the figure will lie between 2 cm^3 and 4 cm^3.

Homework Equations

The Attempt at a Solution

I define the base width as x, then the length is 2x, height as y, then I write the height in terms of x I have the equation: 4x + 8x + 4y = 40. So y = 10-3x.

Now I solve one side of the inequality

x(2x)(10-3x) = 4

and end up with 10x^2 - 3x^3 - 2 = 0

And can't find any whole roots.

There probably aren't any. What they probably want you to do is graph the equation V = -6x³ + 20x² and find the interval(s) on which 3 <= V <= 4.