Question

Design a cylindrical can (with a lid) to contain 5 liters (= 5000 cm3) of water,...

Design a cylindrical can (with a lid) to contain 5 liters (= 5000 cm3) of water, using the minimum amount of metal. What is the diameter and height?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Volume of cylinder is given by

The volume of the cylindrical can to be designed is 5000 cm3.

We can this relation in the surface area formula for cylinder.

  

To find the minimum value of SA, we need to find the critical point of the function SA.

So, the diameter is (2 x 9.267) cm = 18.534 cm.

Height is given by

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A cylindrical metal can is to have no lid. It is to have a volume of...
A cylindrical metal can is to have no lid. It is to have a volume of 27? in^3 . What height minimizes the amount of metal used?
A cylindrical can is built to store a food. This can is constructed without a lid...
A cylindrical can is built to store a food. This can is constructed without a lid and must contain 100cm3 of volume. Find the radius and height of this cylinder so that the amount of material used in its manufacture is minimal.
A new junk food — PopKorn — is to be sold in large cylindrical metal cans...
A new junk food — PopKorn — is to be sold in large cylindrical metal cans with a removable plastic lid instead of a metal top. The metal side and bottom will be of uniform thickness, and the volume is fixed to be 64π in^3 . What base radius r and height h for the can will require the least amount of metal? Show work, and include an argument to show your values for r and h really give a...
A cylindrical can, open at the top, is to hold 220 cm3 of liquid. Find the...
A cylindrical can, open at the top, is to hold 220 cm3 of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent ?.
A cylindrical can, open at the top, is to hold 830 cm3 of liquid. Find the...
A cylindrical can, open at the top, is to hold 830 cm3 of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent π
PROBLEM: A cylindrical can is to be made to hold 50 cm3 of oil. Determine the...
PROBLEM: A cylindrical can is to be made to hold 50 cm3 of oil. Determine the dimensions of the can that will minimize its surface area. What is the minimum surface area?
A cylindrical can open at the top is to have volume 24, 000π cm3 . The...
A cylindrical can open at the top is to have volume 24, 000π cm3 . The material for the base of the can costs three times as much as the material for the rest of the can. What are the dimensions of the can of minimum cost?
A company wants to design an open top cylindrical bin with volume of 250 cm3. What...
A company wants to design an open top cylindrical bin with volume of 250 cm3. What dimensions, which are the radius r and height h, will minimize the total surface area of the bin? Round to one decimal place. (hint: consider bin disassembled for area of the side) Geometry formulas: Area of a circle is ? = ??2, Volume of a cylinder is ? = ??2h, and circumference of a circle is ? = 2??. Use ? = 3.14
4) A fire hose can shoot a stream of water to a maximum height of 20.0...
4) A fire hose can shoot a stream of water to a maximum height of 20.0 m, and the diameter of the stream of water leaving the hose is 3.00 cm. What minimum power is required to sustain such a stream?
1. Three objects have the same volume, one spherical, one rectangular, and the other cylindrical. If...
1. Three objects have the same volume, one spherical, one rectangular, and the other cylindrical. If you put these 3 objects under water, how do their buoyant upward forces compare? A. According to Archimedes’ Principle, they are all subject to the same amount of buoyant forces because they have the same volume B. The cylindrical object gets the most buoyant force because it has a longer shape C. The rectangular object gets the most buoyant force because of its flat...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT