Games
Problems
Go Pro!

# Melting a Golden Cube

Pro Problems > Math > Calculus > Differential > Max and Min

## Melting a Golden Cube

1 cubic foot of gold is melted down and molded into a cylinder. If the cylinder is to have the minimum possible surface area, what will the cylinder’s radius be?

Presentation mode
Problem by Mr. Twitchell

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem

## Similar Problems

### Paint and Framing

An art store struggles to compete against online retailers. Therefore, they choose to sell some of their supplies at a loss, recognizing that it's the only way to get customers in the store. By experimentation, they discover that if they sell tubes of paint at a loss of L cents per tube, they will get 2L2 customers in the store each day, with each customer purchasing (on average) 3 tubes of paint. Of those customers,
L
5
will then purchase a custom framing job. If each custom framing job results in a \$20 profit for the store, how much should the art store discount tubes of paint?

### Height of Launch

A model rocket is launched from a launch pad, and reaches its maximum speed 0.5 seconds into its flight (when the fuel is depleted). At this point, the rocket is 150 feet off the ground, and has a velocity of 400
ft
s
. Its height off the ground at that point is given by the following formula, in which h represents the height in feet, and t represents the amount of time elapsed after fuel depletion.

h(t) = 150 + 400t - 16.1t2

What is the maximum height the rocket attains before it begins to fall to the earth?

### Maximizing xy^2

x and y add to 12.  Find x so that the product xy2 is maximized on the interval 0 < x < 12

### Cost of a Can

A can is required to have a volume of 150p cubic centimeters. The cost of producing the top and bottom is \$0.001 per square cm, and the cost of producing the side is \$0.0008 per square cm. What will be the radius of the can which meets the volume criteria, but costs the least to produce? What will be the price of producing this can?

A quadratic function has a maximum at (1,5,2.5), and crosses the y-axis at y = -2. Find the function.

### Two Big Pig Pens

Farmer Jones has 3000 feet of fencing material. He wants to use this fencing material to create two rectangular pig pens that share a common side, and such that one of the pens is twice the area as the other. He wants to maximize his area. What dimensions should he use for the two pig pens?

# Featured Games on This Site

Match color, font, and letter in this strategy game
Trap all the dots in this problem-solving puzzle

# Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.