Tuesday

March 3, 2015

March 3, 2015

Posted by **Jacob** on Friday, March 8, 2013 at 4:55pm.

Height:

Length:

Width:

- Applied Calculus -
**Reiny**, Friday, March 8, 2013 at 6:25pmbase = 7- 2x

height = x

volume = x(7-2x)^2

= 49x - 28x^2 + 4x^3

d(volume)/dx = 49 - 56x + 12x^2

= 0 for a max volume

12x^2 - 56x + 49 = 0

x = (56 ± √784)/24

= (56 ± 28)/24 = 3.5 or 7/6 or 1.1666...

but clearly x < 3.5 or we have cut the whole base away.

base is 7 - 2(7/6) = 14/3 by 14/3

and the height is 7/6

round to your required decimals

- Applied Calculus -
**Damon**, Friday, March 8, 2013 at 6:28pmnew length = 7 - 2 h

height = h

volume = (7-2h)(7-2h)(h)

v = (49 -28 h + 4 h^2)h

so

v = 4 h^3 -28 h^2 + 49 h

dv/dh = 0 for max or min

dv/dh = 12 h^2 -56 h + 49 = 0

(6h -7)(2 h -7) = 0

h = 7/6 or h = 7/2

if h = 7/2, the box has zero bottom

so the answer is h = 7/6

7 - 2(7/6) = 7-7/3 = 14/3 = length and width

**Answer this Question**

**Related Questions**

Calculus - an open top box is to be made by cutting congruent squares of side ...

calculus - By cutting away identical squares from each corner of a rectangular ...

calculus optimization problem - by cutting away identical squares from each ...

math - a square sheet of tin 30cm on a side is to be used to make an open - top ...

Calculus - By cutting away identical squares from each corner of a rectangular ...

maths - an open box of rectangular base is to be made from 24 cm by 45cm ...

math - By cutting away identical squares from each corner of a rectangular ...

PRE-CALCULUS - AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF ...

calc - an open box is to be made from a 4 ft by 5 ft piece of cardboard by ...

calculus - An open box is to be made from a 21 ft by 56 ft rectangular piece of ...