Question: You wish to construct an observatory, which is shaped like a cylinder with a hemispherical dome on top. The material for the walls of the

You wish to construct an observatory, which is shaped like a cylinder with a hemispherical dome on top. The material for the walls of the cylinder costs $100 per square foot, while the material for the domed roof costs $200 per square foot. The total volume of the observatory needs to be 2000 cubic feet. What dimensions minimize the cost? (Hint: the volume of a sphere of radius r is 4r2.) Remember to include units!

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

You wish to construct an observatory, which is shaped like a cylinder with a hemispherical dome on top. The material for the walls of the cylinder costs $100 per square foot, while the material for...

Q:

2 -1 -3 . . 11z . L . . . For the above rational function f( x ) = , identify its three inflection points. f ' 25224+ 1.5 lowest = ' middle = \\ | highest = r Let f(z) = z 922 2. Calculatg the...

Q:

2 -1 -3 . . 11z . L . . . For the above rational function f( x ) = , identify its three inflection points. f ' 25224+ 1.5 lowest = ' middle = \\ | highest = r Let f(z) = z 922 2. Calculatg the...

Q:

2 -1 -3 . . 11z . L . . . For the above rational function f( x ) = , identify its three inflection points. f ' 25224+ 1.5 lowest = ' middle = \\ | highest = r Let f(z) = z 922 2. Calculatg the...

Q:

please help! very confused! Need help with the investor requirements The new product, if you decide to build it, and if selected by the client, will have a production requirement of 50 units in the...

Q:

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Q:

Due Week 4: Work Breakdown Structure According to the PMBOK Guide, "the WBS is a deliverableoriented hierarchical decomposition of the work to be executed by the project team, to accomplish the...

Q:

MInbox (1,173) x + Question 2 Part 3 of 3 Attempts Remaining: 2 Submit Answer Among various ethnic groups, the standard deviation of heights is known to be approximately 2.8 inches. We wish to...

Q:

15. Suppose there exists a European call option with a strike price of $20 and a premium of $3. There also exists a European put option on the same security with the same $20 strike price and premium...

Q:

15. Suppose there exists a European call option with a strike price of $20 and a premium of $3. There also exists a European put option on the same security with the same $20 strike price and premium...

Q:

Ed Koehler started Great Southern Furniture five years ago to assemble prefabricated bedroom furniture for large hotel chains. Hotels purchase furniture (beds, night stands, and chests of drawers)...

Q:

Lehne Company, which has only one product, has provided the following data concerning its most recent month of operations: Selling price ...............$112 Units in beginning inventory .........500...

Q:

Suppose a particle moves in a straight line and its velocity at time t second is v ( t ) = 4 t 3 3 6 t 2 + 7 2 t ( cm / s ) . Find the displacement of the particle as t varies in the interval 0 t 7

Q:

Nunn Company, which sells electric razors, had $200,000 of cost of goods sold during the month of June. The company projects a 5 percent increase in cost of goods sold during July. The inventory...

Q:

Lumpkin Company sells lamps and other lighting fixtures. The purchasing department manager prepared the following inventory purchases budget. Lumpkin's policy is to maintain an ending inventory...

Q:

The budget director of Heather's Florist has prepared the following sales budget. The company had $50,000 in accounts receivable on July 1. Heather's Florist normally collects 100 percent of accounts...

Q:

Parliament Company, which expects to start operations on January 1, 2018, will sell digital cameras in shopping malls. Parliament has budgeted sales as indicated in the following table. The company...

Q:

Two items are omitted in each of the following four lists of income statement data. Determine the amounts of the missing items, identifying them by letter. Sales Cost of merchandise sold Gross profit...

Q:

A pointer holds a memory address.

Q:

3. List four points that you think are important to give the individual attention, when he or she is going to sell an argument or an idea to you.

Q:

4. Think of a situation where you would convince someone of an argument or an idea you had. a. What feelings did you want the other person to be left with when you finished? b. When you think about...

Q:

7. Think of a situation where you felt that you mastered the situation, i.e. where you had a positive feeling of completing the task you were to perform. A. Now develop a picture in your imaginary...