1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nataliya [291]
3 years ago
11

A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amo

unt of cardboard.
Mathematics
1 answer:
Blababa [14]3 years ago
8 0

Answer:

<h2><em>2ft by 2ft by 1 ft</em></h2>

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>

You might be interested in
Diego solved an equation by multiplying both sides of the equation by 6. Then he checked that 6 is the correct solution by subst
Studentka2010 [4]
C.      on e2020 . Good luck!
6 0
3 years ago
Help please !!!
slava [35]
C is the best answer choice
8 0
2 years ago
Find the values of the variables and lengths of the sides of this kite.<br> Y-3, x+5, 2x+5, x+10
zzz [600]
Y=3
x=-5
x=-5/2
x=-10
.....................
4 0
3 years ago
Read 2 more answers
How you turn 4 and 1/2 into a decimal
Nat2105 [25]
Four and half would be 4.5 because your whole number is four and half of one would be .5
3 0
3 years ago
Read 2 more answers
Which best models a plane ? A. a floor B. A pebble C. a jump rope D. a stick
swat32
A. a floor. Because it is very flat than the other ones.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Kaitlin, Hans, Eric went a total of 98 Text messages during the weekend. Kaitlin 68 more messages than Hans, Eric sent three tim
    11·2 answers
  • Plz help<br><img src="https://tex.z-dn.net/?f=%20" id="TexFormula1" title=" " alt=" " align="absmiddle" class="latex-formula">
    15·1 answer
  • Graph the set of points. which model is most appropriate for the set (-6 4) (-4 0) (-3 -2) (-1 -7)
    6·1 answer
  • What are the first 5 multiples of 15?
    10·2 answers
  • How do I know if l -27 l in is less or greater than -45 ​
    15·1 answer
  • A criminal has escaped in a train wreck. The police believe he could have traveled no more than 7 mi in any direction from the w
    6·1 answer
  • Asap please help! and explain how you got the answer!
    8·1 answer
  • Find the slope of the line.
    12·2 answers
  • What are the solutions of the equation 4x2 + 3x = 24 – x?
    5·1 answer
  • A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and e
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!