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
Trava [24]
2 years ago
5

An open box with a square base is to have a volume of 4000in3. Find the length of the side of the square base that would result

in the least amount of material needed to construct the box.
Mathematics
1 answer:
Elina [12.6K]2 years ago
7 0

Answer:

I did this quickly and don't have the time to check.  Please review carefully.

Length of the side of a square base to provide a volume of 4000 in^3 with the minimum material to construct the entire box. is 6 in.  The dimensions for this box would be (6 in) by (6 in) by 111.1 in.

Step-by-step explanation:

The volume of a square box is given by

Volume(V) = L*W*H,

where L is length, W is width, and H is height.

Since the base is square, W = L, so we can rewrite the volume equation as:

V = L*W*H

V = L*L*H

Volume = L^2H

The area of the box surface is the sum of all the sides:

Top and Bottom:    2*(L*W), or 2 (W^2)

2 Sides:                  2*(W*H), or 2(W^2)

2 other sides:        2*(L*H)  

The total surface area is

  Area = 2*(L*W) + 2*(W*H) +  2*(L*H)

Since W=L, we can rewrite this equation as:

  Area = 2*(L*L) + 2*(L*H) +  2*(L*H)

<u>Total Surface Area = 2L^2 + 4LH</u>

The target volume is 4000 in^3

We know that Volume = L^2H from above.

4000 in^3 = L^2H

we can rewrite this as:

H = 4000/L^2

Substitute this value of H into <u>Total Surface Area = 2L^2 + 4LH</u>

Total Surface Area = 2L^2 + 4L(4000/L^2)

Total Surface Area = 2L^2 + (1000/L)

We want to minimize total surface are, so we can either plot this function and look for the minimum, or we can take the first derivative and set it equal to zero (the first derivative tells us the slope of the line at any point.  We want the point where the slope is zero, where it changes direction).  I will plot the function.

<u>Plot: </u> See attached graph.

I set the above equation to the format:  y = 2x^2 + (1000/x), where y is the total surface area and x is the box length.

I see a minimum at (6.2,230).  This corresponds to a box length of 6.2 in and a surface area of 230 in^2.

You might be interested in
Find the median and mode of the data.
jeka94

Answer:the mode is 2 1/2 because it repeats twice

Step-by-step explanation:repeats twice

4 0
3 years ago
Using a property of operations, what can you say about the sums of (-13.2) + 8.1 and 13.2 + (-8.1)
Wewaii [24]
They are opposites of each other.
-13.2 + 8.1 = -5.1
13.2 - 8.1 = 5.1
4 0
3 years ago
HELP PLZ!! Convert 80 mph (miles per hour) to feet per second.
marin [14]

Answer:

117.33333 feet per second

Step-by-step explanation:

6 0
2 years ago
HOW MANY BASEBALLS CAN FIT INTO THE TRACTOR TRAILER. THE TRAILER DIMENSIONS ARE 301.5"L X 96.99"W X 105.04"H AND CIRCUMFERENCE R
Shkiper50 [21]
Volume of tractor = length x width x height = 301.5 x 96.99 x 105.04 = 3,071,630.624

For baseballs of 9 inches:
9=2\pi r \\  \\ r= \frac{9}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9}{2\pi} \right)^3=12.31

Number of 9 inches baseballs = \frac{3,071,630.624}{12.31} = 249,513

For baseballs of 9.25 inches:
9.25=2\pi r \\  \\ r= \frac{9.25}{2\pi}

Volume = \frac{4}{3} \pi r^3= \frac{4}{3} \pi \left( \frac{9.25}{2\pi} \right)^3=13.37

Number of 9.25 inches baseballs = \frac{3,071,630.624}{13.36} = 229,824

Therefore, the tractor can contain between 229,824 and 249,513 baseballs.
8 0
2 years ago
What is the slope of the line through (2,-2)and(9,3)?
Arturiano [62]

Answer:

5/7

Step-by-step explanation:

y2-y1/x2 -x1

3 - (-2)/9-2

3+2/9-2

5/7

4 0
3 years ago
Read 2 more answers
Other questions:
  • How are your suppose to simplify 4y-y
    14·2 answers
  • -44 + 27 =help..................................
    6·2 answers
  • If f(x) = <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20" id="TexFormula1" title=" x^{2} " alt=" x^{2} " align="absmiddle"
    7·1 answer
  • Which shows the commutative property?
    12·2 answers
  • *PLEASE ANSWER, DIFFICULT QUESTION, ASAP* An ice cream machine offers three flavors: vanilla, chocolate, and strawberry. Each fl
    5·1 answer
  • What is the probability that the system does not have a type 2defect?b.What is the probability that the system has both type 1 a
    6·1 answer
  • In a triangle ABC with |AB|=9m,|AC| =6m ,the sides AB and AC are produced to points X and Y respectively such that angleBXY=62°,
    10·1 answer
  • PLEASE HELP ME WITH THIS
    6·2 answers
  • Plzzzz answer fast..​
    6·1 answer
  • Triangle KNM is shown. Triangle K N M is shown. Angle M K N is 25 degrees. Angle K N M is 130 degrees. Angle N M K is 25 degrees
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!