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
diamong [38]
3 years ago
13

An engineer must design a rectangular box that has a volume of 9 m3 and that has a bottom whose length is twice its width. What

are the dimensions of the box so that the total surface area (of all six sides) of the box is minimized
Engineering
1 answer:
Jet001 [13]3 years ago
6 0

Answer:

Length =3   Height = 2   and  Width = \frac{3}{2}

Explanation:

Given

Volume = 9m^3

Represent the height as h, the length as l and the width as w.

From the question:

Length = 2 * Width

l = 2w

Volume of a box is calculated as:

V = l*w*h

This gives:

V = 2w *w*h

V = 2w^2h

Substitute 9 for V

9 = 2w^2h

Make h the subject:

h = \frac{9}{2w^2}

The surface area is calculated as:

A = 2(lw + lh + hw)

Recall that: l = 2w

A = 2(2w*w + 2w*h + hw)

A = 2(2w^2 + 2wh + hw)

A = 2(2w^2 + 3wh)

A = 4w^2 + 6wh

Recall that: h = \frac{9}{2w^2}

So:

A = 4w^2 + 6w * \frac{9}{2w^2}

A = 4w^2 + 6* \frac{9}{2w}

A = 4w^2 + \frac{6* 9}{2w}

A = 4w^2 + \frac{3* 9}{w}

A = 4w^2 + \frac{27}{w}

To minimize the surface area, we have to differentiate with respect to w

A' = 8w - 27w^{-2}

Set A' to 0

0 = 8w - 27w^{-2}

Add 27w^{-2} to both sides

27w^{-2} = 8w

Multiply both sides by w^2

27w^{-2}*w^2 = 8w*w^2

27 = 8w^3

Make w^3 the subject

w^3 = \frac{27}{8}

Solve for w

w = \sqrt[3]{\frac{27}{8}}

w = \frac{3}{2}

Recall that : h = \frac{9}{2w^2}   and l = 2w

h = \frac{9}{2 * \frac{3}{2}^2}

h = \frac{9}{2 * \frac{9}{4}}

h = \frac{9}{\frac{9}{2}}

h = 9/\frac{9}{2}

h = 9*\frac{2}{9}

h= 2

l = 2w

l = 2 * \frac{3}{2}

l = 3

Hence, the dimension that minimizes the surface area is:

Length =3   Height = 2   and  Width = \frac{3}{2}

You might be interested in
Atoms contain charged particles called___?
solong [7]

Answer:

Answer;

protons and electrons

4 0
3 years ago
Explain why Didymos B is an ideal asteroid for testing the DART system.​
Yanka [14]

Answer:

Rhe fact that Didymos B is in orbit around Didymos A makes it easier to see the results of the impact, and ensures that the experiment doesn't change the orbit of the pair around the sun.” After launch, DART would fly to Didymos, and use an on-board autonomous targeting system to aim itself at Didymos B

Explanation:

8 0
4 years ago
The inlet for a high-bypass-ratio turbofan engine has an area A1 of 6.0 m 2 and is designed to have an inlet Mach number M~ of 0
Lelu [443]

Answer:

The additive drag at flight condition will be found by the following equation

Area = A1 = 6m2

Da = Additive drag

Cda = Additive drag coefficient

P = prassure at altitude of 12Km

Po = Prassure at sea level

 \gamma = Ratio of specific heat capacity

The formula of additive drag is given below

D = Cda q A

q = Dynamic prassure , A = cross sectional area

q =( \gamma/ 2) P0 M02

    D = Cda ( \gamma/2) po Mo2 A

Cda=0.32

 \gamma=1.4

M=0.8

p0= 101325pa

D = 0.32 (1.4/2)(101325pa)(0.6)2 6

D = 49025N

Explanation:

The additive drag at the flight conditions will be D= 49025N

8 0
3 years ago
This is used to keep all cleaning supplies and chemicals safe
bulgar [2K]
A storage room




common sense lol
6 0
3 years ago
Pre Test
OverLord2011 [107]

Answer:

a is greater torgue

please make brainlist

8 0
3 years ago
Other questions:
  • Water enters a circular tube whose walls are maintained at constant temperature at specified flow rate and temperature. For full
    8·1 answer
  • What is the thermal efficiency of a gas power cycle using thermal energy reservoirs at 627°C and 60°C? The thermal efficiency is
    12·1 answer
  • An engineer is working with archeologists to create a realistic Roman village in a museum. The plan for a balance in a marketpla
    9·1 answer
  • Show that a chirped Gaussian pulse is compressed initially inside a single-mode fiber when ftC < 0. Derive expressions for th
    12·1 answer
  • According to the video, what are some of the effects of the increase in the use of automated tools for Loading Machine Operators
    11·2 answers
  • 7. The "3 second rule" is the time you should pause at an intersection marked with a stop sign.
    6·1 answer
  • The function below takes a single argument: data_list, a list containing a mix of strings and numbers. The function tries to use
    10·1 answer
  • 2. The block is released from rest at the position shown, figure 1. The coefficient of
    9·1 answer
  • Technician A states that a brake lathe is used to make a used brake rotor surface "like new". Technician B states that a brake l
    7·1 answer
  • 1. What's an object in your everyday life that has a lot of Kinetic Energy? How do you know it has a lot?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!