Wednesday

September 17, 2014

September 17, 2014

Posted by **Valerie Pacetti** on Friday, January 21, 2011 at 4:02am.

values of x that maximizes volume = in

Maximum volume= in^3

- College Algebra -
**Dr Russ**, Friday, January 21, 2011 at 6:39amI would start with a drawing as I do for most problems. Draw a reactangle 4x one side and b the other.

The perimeter is then 4x+b+4x+b=11

8x+2b=11

if this is folded to a tube then the volume of the tube is bx^2, i.e. a tube with cross sectional area x^2 and length b.

so V=bx^2

rearrangen and substitute for b into the equation above gives

8x+2V/(x^2) = 11

or

8x^3+2V=11x^2

or

V=5.5x^2-4x^3

which you can plot to find max V

I got 1.54 in^3 as the max volume

but check the maths!

**Answer this Question**

**Related Questions**

math - On a rectangular piece of cardboard with perimeter inches, three parallel...

geometry - On a rectangular piece of cardboard with perimeter 11 inches, three ...

Geometry - On a rectangular piece of cardboard with perimeter 11 inches, three ...

math - in a rectangular with a perimeter of 30 inches two parallel and equally ...

Geometry - Ok Dr. Russ helped me find one part of the question, but I still can'...

math - in a rectangular with a perimeter of 30 inches two parallel and equally ...

Math- Math Analysis - In a rectangular piece of cardboard with a perimeter of ...

Algebra - A rectangular piece of cardboard is 15 inches longer than it is wide. ...

Calculus - Squares with sides of length x are cut out of each corner of a ...

Algebra - You have to make a square-bottomed, unlidded box with a height of ...