Posted by sadia khan on Saturday, January 19, 2013 at 2:42am.
an open box of rectangular base is to be made from 24 cm by 45cm cardboard by cutting out squares sheets of equal size from each corner and bending the sides.find the dimensions of the corner squares to obtain a box having largest volume.

maths  Reiny, Saturday, January 19, 2013 at 8:53am
let each side of the cutout square be x cm
where 0 < x < 12
base of box is (242x) by (452x)
height will be x
volume = x(242x)(452x)
= x(1080  138x + 4x^2) = 4x^3  138x^2 + 1080x
d(volume)/dx = 12x^2  276x + 1080
= 0 for a max/min of volume
x^2  23x + 90 = 0
(x18)(x5) = 0
x = 18 or x = 5
but x < 12 , so x = 5
a square of 5 by 5 cm should be cut out.
test:
if x = 4.8
volume = 4.8(249.6)(459.6) = 2446.848
if x = 5
volume = 5(2410)(4510) = 24050
if x = 5.1
volume = 5.1(2410.2)(4510.2) = 2449.224
max when x=5
Answer This Question
Related Questions
 math  An open box is made from a rectangular piece of cardboard, with ...
 math  An opentopped box is made from a rectangular piece of cardboard, with ...
 Math  A Candy box is made from a piece of cardboard that meaasures 11 by 7 ...
 PreCal  A square sheet of cardboard 18 inches is made into an open box (there ...
 calculus  An open box is to be made out of a 8inch by 14inch piece of ...
 Calc  An open box is to be made out of a 10inch by 16inch piece of cardboard ...
 Calculus 1  A box with an open top is to be constructed from a rectangular ...
 Math  A box with an open top is to be constructed from a rectangular piece of ...
 calculus  An open box is to be made out of a 10inch by 14inch piece of ...
 Maths  a rectangular metal sheet of length 30cm and breadth 25cm is to be made ...
More Related Questions