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
Vlad [161]
3 years ago
5

What are the dimensions of the lightest​ open-top right circular cylindrical can that will hold a volume of 2197 cm cubed​?

Mathematics
1 answer:
Zarrin [17]3 years ago
4 0

Answer:

  radius = height ≈ 8.88 cm

Step-by-step explanation:

If the weight is proportional to the surface area, then we need to find the minimum surface area for the given volume.

The volume of the can is given by ...

  V = πr²h . . . . . . for radius r and height h

The surface area includes that of the bottom and the sides:

  SA = πr² +2πrh

Solving the first equation for h, we can write the second equation as ...

  SA = πr² +2πr(V/(πr²)) = πr² +2V/r

__

The minimum area for the volume will be found where the derivative is zero.

  d(SA)/dr = 2πr -2V/r² = 0

  πr³ = V . . . . . multiply by r²/2 and add V

Then the can radius is ...

  r = ∛(V/π)

and the height is ...

  h = V/(π(V/π)^(2/3)) = ∛(V/π) = r

__

For the given volume, the dimensions are ...

  r = h = ∛(2197/π) ≈ 8.8762 cm

The lightest can with that volume has a radius and height of about 8.88 cm.

_____

<em>Comment on cylinder aspect ratio</em>

You may notice that the lateral area is equal to twice the bottom area for this cylinder. If the can had a top, the minimum weight would be such that the lateral area is twice the total of top and bottom area. In that case, the height is equal to the diameter, not the radius.

You might be interested in
Trevor ran 2.3 miles on Monday and then ran some more on Tuesday, he had run a total of 5.55 miles for the week. How much did he
KiRa [710]

Answer:

He ran 3.25 on Tuesday

Step-by-step explanation:

The answer is 3.25 because 5.55 minus 2.3 is 3.25.

5 0
3 years ago
Read 2 more answers
Malcolm is filling bags with rice. He starts with a 5 1/4 pound container of rice and fills each
Sliva [168]

Basically we want to know how many times 5/8 goes into 5 1/4.

5 1/4 ÷ 5/8 = 21/4 ÷ 5/8 = 21/4 × 8/5 = 42/5 = 8.4 bags

Since we cannot have a fraction of a bag, he can fill 8 bags completely.

answer: 8 bags

6 0
3 years ago
The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit
Alla [95]

Answer:

The answer is below

Step-by-step explanation:

The diameter of a tire is 2.5 ft. a. Find the circumference of the tire. b. About how many times will the tire have to rotate to travel 1 mile?

Solution:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation = \frac{5280\ ft}{7.85\ ft\ per\ rotation}=672\ rotations\\\\\\

4 0
2 years ago
Read 2 more answers
Algebra
vladimir2022 [97]
(2x + 3y = 12) x (-2)
(4x - 3y = 6) x 1

-4x - 6y = -24
4x - 3y = 6

You can cancel out the x values by adding the two equations together. 
(-4x + 4x) + (-6y - 3y) = (-24 + 6)
-9y = -18
y = 2

Solve for x now...
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3

Check... (x = 3, y = 2)
2(3) + 3(2) = 12 
6 + 6 = 12
12 = 12 <- this works! 

4(3) - 3(2) = 6
12 - 6 = 6
6 = 6 <- this works!
5 0
2 years ago
Read 2 more answers
First answer gets brainliest!!!!! Please help
maw [93]

Answer: first answer

:))))))))))))))))))

Where my brainlist

4 0
2 years ago
Read 2 more answers
Other questions:
  • Write declaration statements to declare and initialize two variables: one is an integer variable named age, initialized to 18, a
    13·1 answer
  • What is the distance between point L (8,9) and Z (-10,0), to the nearest tenth of a unit
    7·1 answer
  • Is 3.667 a rational number,interger,or whole number
    11·1 answer
  • From a box containing 6 black balls and 4 green balls, 3 balls are drawn in succession, each ball being re- placed in the box be
    14·1 answer
  • A given data set has: A mean of 26.5 An interquartile range of 5.5 A minimum of 21 And a maximum of 29 What measure describes al
    11·1 answer
  • A map has a scale of 1 in: 10 mi. On the map, the distance between two cities is 5 inches. What is the actual distance between t
    8·1 answer
  • Please solve I’m confused
    8·2 answers
  • louie has $1,000 and wants it to grew to $5,000 in 10 years,what compound interest rate does he need?
    11·1 answer
  • What is 2/2 minutes that’s added to 2/3
    11·1 answer
  • 1.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!