Derivative Word Problem Help Please!~

An observatory is to be in the form of a right circular cylinder surmounted by a hemispherical dome. If the hemispherical dome costs 6 times as much per square foot as the cylindrical wall, what are the most economic dimensions for a volume of 16000 cubic feet?

The radius of the cylindrical base (and of the hemisphere) is _____ ft. (Round to the nearest tenth).

Re: Derivative Word Problem Help Please!~

Here are some questions to help guide you. What are the equations of surface area for the lateral surface area of a cylinder, and that of a hemisphere? What would be the cost of the cylindrical part if the cost was C per ft^2 (if you need more help: you want to buy 2 kg of apples and the price is $3 per kg: what do you do to these two numbers to figure out the total cost?) Post your answers and further questions below and we'll go from there.

Re: Derivative Word Problem Help Please!~

Quote:

Originally Posted by

**majamin** Here are some questions to help guide you. What are the equations of surface area for the lateral surface area of a cylinder, and that of a hemisphere? What would be the cost of the cylindrical part if the cost was C per ft^2 (if you need more help: you want to buy 2 kg of apples and the price is $3 per kg: what do you do to these two numbers to figure out the total cost?) Post your answers and further questions below and we'll go from there.

π = pi

Area: A = 2πr^{2}+2πrh

C = (6)2πr^{2}+2πrh

Cost: C = (32000/r) + (72πr^{2}/3)

This could be wrong.. I'm not very good with these word problems. Are these equations correct?

Re: Derivative Word Problem Help Please!~

Re: Derivative Word Problem Help Please!~

Okay I think I got it now! Thank you so very much!