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
patriot [66]
3 years ago
14

A circular cylindrical container, open at the top, and having a capacity of 24pi cubic inches, is to be manufactured. If the cos

t of the material used for the bottom of the container is three times that used for the curved part and if there is no waste of material, find the dimensions which will minimize the cost
Mathematics
1 answer:
otez555 [7]3 years ago
5 0

Answer: radius r = 2 inches

height h = 6 inches

Step-by-step explanation:

Given;

Volume V = 24πin3

Volume of a cylinder is given by

V = πr^2h

h = V/πr^2. ....1

Where, h = height and r = radius of cylinder

For the surface area of the cylinder with open top. we have,

S = 2πrh + πr^2

For the cost of materials used, let k represent the cost of materials used for the body of the cylinder.

Then, for the bottom will be 3k

Total cost will be represented by C, which gives

C = 2πrhk + 3πr^2k. .....2

Substituting eqn 1 to 2, we have;

C = 2πrVk/πr^2 + 3πr^2k

C = 2Vk/r + 3πr^2k

The material cost is minimum at dC/dr = 0

dC/dr = -2Vk/r^2 + 6πrk =0

6πrk = 2Vk/r^2

r^3 = 2V/6π

r = (2×24π/6π)^-3

r = (8)^-3

r = 2

Substituting r = 2 into eqn1

h = 24π/π(2^2)

h = 24/4 = 6

h = 6

You might be interested in
Find the center and radius of the circle (x+3)^2+(y-1)^2=81
sasho [114]

The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2

h and k is the center point of the circle and r is the radius.

In the given equation (x+3)^2 + (y-1)^2 = 81

h = -3

k = 1

r^2 = 81

Take the square root of both sides:

r = 9

The center is (-3,1) and the radius is 9

5 0
3 years ago
The set of types of matter<br>well difined or not​
Tresset [83]

Answer:

It is not well defined.

Step-by-step explanation:

Because set is a collection of well defined objet. And matter contains of solid, liquid and gas

3 0
3 years ago
Find pb, if pj=14 and jb= 28
anyanavicka [17]

Answer:

42

Step-by-step explanation:

Based on the information given, point j is the midpoint, as it is shared by both line segments. Set the equation:

pb = pj + jb

Note:

pj = 14

jb = 28

Plug in the corresponding numbers to the corresponding variables:

pb = pj + jb

pb = 14 + 28

pb = 42

pb = 42 is your answer.

~

3 0
3 years ago
Read 2 more answers
lamars bowling scores were 124, 150, and 161, during league competition. if lamars previous bowling average was a 129, how much
Darina [25.2K]
43 is the correct answer


8 0
3 years ago
Read 2 more answers
What are the vertices of /(△)?
Serga [27]

Answer:

3!

Step-by-step explanation:

The vertices are the points of the triangle. So if you count each point you get 3!

8 0
3 years ago
Read 2 more answers
Other questions:
  • A cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. The resulting cross se
    13·2 answers
  • 1. A fence needs replacing to properly secure a barn. The section to be fenced is a 120 metres by 36
    12·1 answer
  • Is the answer for number 3 solution or open sentence?
    6·1 answer
  • Please hurry i need an answer fast i don’t know this one?!!!!??
    14·2 answers
  • If 4 over 9 equals 2 over x , what do you know about their cross products?
    14·1 answer
  • If AB has a midpoint, the AB is<br> Select one:<br> a. a line segment <br> b. a line <br> c. a ray
    7·1 answer
  • HELPPP PLSSS!!!!!!!!
    6·1 answer
  • NAME THE SOLID SHAPE PLEASE SOMEONE HELP ME!!!
    8·2 answers
  • What is √ 63 − 4 √ 7??
    8·1 answer
  • Which table represents the statement "Brian rides a bicycle at a rate of 12 meters per second"?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!