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
mixer [17]
3 years ago
5

Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui

lding material possible.
Mathematics
1 answer:
Vesnalui [34]3 years ago
3 0
<h3>The dimensions of the given rectangular box are:</h3><h3>L  =   15.874 cm  , B  =  15.874 cm   , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box  

= Area of the base +  4 x ( Area of the adjacent faces)

=  S x S  +  4 ( S x H)   = S² +  4 SH   ..... (1)

Also, Area of the box  = S x S x H  =  S²H

⇒ S²H = 2000

\implies H = \frac{2000}{S^2}

Substituting the value of H in (1), we get:

A = S^2 + 4 SH =  S^2 + 4 S(\frac{2000}{S^2}) =  S^2 + (\frac{8000}{S})\\\implies A  =  S^2 + (\frac{8000}{S})

Now, to minimize the area put :

(\frac{dA}{dS} ) = 0 \implies 2S  - \frac{8000}{S^2}  = 0\\\implies S^3 = 4000\\\implies S  = 15.874 \approx 16 cm

Putting the value of S  = 15.874 cm in the value of H , we get:

\implies H = \frac{2000}{S^2}  =  \frac{2000}{(15.874)^2} = 7.8937 cm

Hence, the dimensions of the given rectangular box are:

L  =   15.874 cm

B  = 15.874 cm

H = 7.8937 cm

You might be interested in
If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total
Charra [1.4K]

Answer:

  • 394 pages

Step-by-step explanation:

<u>1- digit numbers: </u>

  • 1 to 9, number of digits = 9

<u>2- digit numbers:</u>

  • 10 to 99, number of digits = 2(99 - 9) = 180

<u>3- digit numbers:</u>

  • 100 to 999, number of digits = 3(999 - 99) = 2700

This is more than we have, but we know the number of pages is 3-digit.

<u>Let it be x, then we have:</u>

  • 9 + 180 + 3(x - 99) = 1074
  • 3(x - 99) = 1074 - 189
  • 3(x - 99) = 885
  • x - 99 = 885/3
  • x - 99 = 295
  • x = 295 + 99
  • x = 394
4 0
2 years ago
Zn (s) + Cu2+ (aq) → Cu (s) + Zn2+ (aq)
White raven [17]
The answer is A zinc is oxidized and copper gets reduced
8 0
3 years ago
Read 2 more answers
Your $440 gets 5.8% interest compounded annually for 8 years. What will your
ladessa [460]

Answer:

492.52

Step-by-step explanation:

The formula is P(t) = P(0) x (1+r/n)^nt so...

P(t) = 440 (1+0.058/1)^8

P(t) = 492.52

3 0
3 years ago
7(n+4) ....................
Juli2301 [7.4K]

Answer:

<h2>7n + 28</h2>

Step-by-step explanation:

7(n + 4)

Expand

7 \times n = 7n \\ 7 \times 4 = 28 \\  \\ 7n + 28

4 0
3 years ago
Please help!! ASAP thanks
Brut [27]

Answer:10

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • I need help plz. Thank you
    15·2 answers
  • Graham's sunflower is 2 feet tall. Katie's sunflower is 1 foot 8 inches tall. How much taller is Graham's sunflower?
    14·2 answers
  • Please help. I have been stuck for days now
    7·1 answer
  • On a 10 question exam each question is worth 10 points. how many ways can you make a 70%?
    14·1 answer
  • Can a rational function have vertical and oblique asymptote
    14·2 answers
  • Write the decimal represented by each shaded square.
    10·1 answer
  • Find the x-intercept of the following line. y=5x+20
    8·1 answer
  • (y − 3)^2 = 4(x − 5), (6, 1). Find an equation of the tangent line to the graph at the given point.
    5·1 answer
  • Jane works at The Bottling Company. She needs to put 8,500 bottles of water into cases. So far she has put 2,136 in cases. How m
    15·1 answer
  • What is 5 ÷ 1/5 <br> I really need help with dividing whole numbers by fractions
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!