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
Cerrena [4.2K]
3 years ago
15

If 1000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible

volume of the box.
Mathematics
2 answers:
guapka [62]3 years ago
6 0
<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h: x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x] Simplify and get V = 250x-x^3/4 The volume will be a maximum when its first derivative is 0. V' = 250-3/4x^2 Set to 0 and solve. x=18.26 Now plug into the volume function to find the maximum volume: V=250(18.26)-(18.26)^3/4 V= 4564.35 - 1522.10 =3042.25</span>
laila [671]3 years ago
3 0

Answer:

Maximum volume of the box is 3042.91 cm³

Step-by-step explanation:

Area of the material available to make a box with square base and open top = 1000 square cm.

Total surface area of the box = 2(lh + bh) + l×b

Where l = length of the box

b = width of the box

h = height of the box

If l = b, Total surface area of the box = 2(lh + lh) + l×l

Surface area = 4lh + l² = 1000

l(4h + l) = 1000

4h + l = \frac{1000}{l}

h = \frac{1000}{4l}-\frac{l}{4}

Now volume of the square box = lbh

V = l²h

V = l²(\frac{250}{l}-\frac{l}{4})

V = 250l - \frac{l^{3}}{4}

Now to calculate the maximum volume we have to find the derivative of the volume.

\frac{dV}{dl}=250-\frac{3l^{2} }{4}

By equating derivative to zero,

250 - \frac{3l^{2}}{4} = 0

l = \sqrt{\frac{250\times 4}{3}}

l = 18.26 cm

For l = 18.26, V = 250(18.26) - \frac{(18.26)^{3}}{4}

V = 4565 - 1522.09

  = 3042.91 cm³

Therefore, maximum volume of the box is 3042.91 cm³

You might be interested in
4. The area of a regular hexagon is 50 in. Find the length of a side. Round your answer to the nearest tenth.
Vikki [24]

Answer: 4.4

Step-by-step explanation:

The formula for calculating the area of regular hexagon is given as :

Area = \frac{3\sqrt{3}}{2}a^{2}

Where a is the length of a side.

Substituting the value given , we have :

50 =  \frac{3\sqrt{3}}{2}a^{2}

50 x 2 = 3\sqrt{3} a^{2}

100 = 3\sqrt{3} a^{2}

Divide through by 3\sqrt{3}

a^{2} = \frac{100}{3\sqrt{3}}

a^{2} = 19.24500897

Take the square root of both sides :

a = \sqrt{19.24500897}

a = 4.3869

To the nearest tenth

a = 4.4

4 0
3 years ago
4.5/5.5 simplified ? thanks!
Scrat [10]

Answer:

Step-by-step explanation:

You can multiply the numerator and denominator by 2

(4.5/5.5)(2/2)=9/11

6 0
3 years ago
GIVING BRAINLIEST TO PERSON AHO ANSWERS FIRST!!
zavuch27 [327]
Please refer to the photograph attached for the answer
Hope you find the answers correct
Sorry you will find it really small please zoom in to see the answer to this question
Sorry for the inconvenience about the small answers

4 0
2 years ago
Please help me on this I’m so tired and I can’t sleep until my progress is at 80 and this is the end of my year it’s at 79%
Elena L [17]

Answer:

The answer is the bottom left

4 0
3 years ago
Six friends each het 3/8 of a pound of candy. how much candy will the friends get in all
tamaranim1 [39]
6(3/8)

18/8

9/4

2 1/4 or

2.25 lbs
6 0
3 years ago
Other questions:
  • Name
    15·2 answers
  • Qual sera o valor do juros correspondente a um emprestimo de 15.000 no prazo de 1 ano, 2 meses e 25 dias em uma taxa de juros co
    15·1 answer
  • Number 4 <br> (Which proportion represents the problem below)
    11·1 answer
  • What’s the answer to _-3/4=2/3
    7·2 answers
  • Consider the function represented by the equation y-6x-9 +0. Which answer shows the equation written in function notation
    12·1 answer
  • A group of friends goes out to dinner. The total bill, without tax, is $63. If tax on the meal is 6% and if an 18% tip is left o
    11·1 answer
  • Another submarines dissent can be modeled as Y= -250 X, where why is the vertical position and access time in hours. How long wi
    9·1 answer
  • 6) A linear equation is graphed. What is the y-intercept of the linear<br> equation? *
    6·1 answer
  • What number is 27% of 52? Round to the nearest tenth if necessary.
    7·2 answers
  • Math problems (Easy) <br> ………………………………………..
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!