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
Lelu [443]
3 years ago
6

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

cutting congruent squares from the corners and folding up the sides. Then find the volume.
Mathematics
1 answer:
a_sh-v [17]3 years ago
6 0

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

You might be interested in
After the outbreak of a mysterious disease, the average wait time at a hospital increased by 70\%70%. Before the outbreak, the a
Scilla [17]

Answer:choice A, Choice C.


Step-by-step explanation: 70/%70%/MM


6 0
3 years ago
Read 2 more answers
(2x^4 − 3x^3 − 20x − 21) ÷ (x − 3)
dimaraw [331]
2x^3+3x^2+9x+7 is the  answer
8 0
3 years ago
Whats the answer to this question ?
Andrei [34K]
6 3/7 multiplied by 21 is 135. Your answer is C. 135 <span />
5 0
3 years ago
Read 2 more answers
Convert 111.1 to base 10​
larisa [96]

Answer:

111.1

Step-by-step explanation:

5 0
2 years ago
360 miles in 6 hours
elena-14-01-66 [18.8K]
Just divide 360 and 6 and what ever your answer is you add 1 at the bottom for example if your answer is 12 you write your answer like this 12/1
4 0
3 years ago
Read 2 more answers
Other questions:
  • The present population of a town is 3125. If the population increases
    15·2 answers
  • What is 5 billion times 96 billion ?
    10·1 answer
  • HELP HELP HELP Certain members of the Italian Parliament make 180,000 euros a year. If 1 euro equals 1.36 U.S. dollars, how much
    6·1 answer
  • Choose the adverb and then decide which adjective it modifies in the sentence below.
    8·1 answer
  • Evaluate 3(4-2) what would be the answer to this
    7·2 answers
  • Ken built a square fence around his yard. He planted 5 trees on each side of the fence. What is the least number of trees Ken pl
    9·1 answer
  • Find the 8th term of the sequence
    9·2 answers
  • Write an exponential function y = a(b)" whose graph passes through the given
    5·1 answer
  • Find the value of x<br> −9(10+x)=−243
    11·1 answer
  • Evaluate 4m-7,when m = 5
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!