Simple Word Problem 1 Help !!!

[merikukri]

1.A drum in the shape of a right circular cylinder is required to have a volume of cubic centimeters. The top and bottom are made of material that costs F¢ per square centimeter; the sides are made of material that costs L¢ per square centimeters. (Hint: The formula for the volume of a right circular cylinder is V=pie r^2 , where r is the radius of the circular base and h is the height of the cylinder. The surface area of the sides can be determined by cutting the cylindrical shell vertically and flattening it out to get a rectangle whose dimensions can be determined.)

a)Express the total cost C of the material as a function of the radius r of the cylinder.
b)What is the cost if the radius is 25 cm?
c)Graph C=C(r) . Using the graph, for what value of r, approximately, is the cost C least?
Where F = 5, L =4

 

[stapel]

I'm sorry, but it appears that some information is omitted or obscured. For instance, the "drum...is required to have a volume of ___ cubic centimeters." How many? The number was omitted. And "the top and bottom are made of material that costs [unreadable characters] per square centimeter." The price is obscured.

Please reply with corrections and clarifications, showing how much you have attempted so far. Thank you.

Eliz.

 

[merikukri]

I'm sorry, but it appears that some information is omitted or obscured. For instance, the "drum...is required to have a volume of ___ cubic centimeters." How many? The number was omitted. And "the top and bottom are made of material that costs [unreadable characters] per square centimeter." The price is obscured.

Please reply with corrections and clarifications, showing how much you have attempted so far. Thank you.

Eliz.

I am sorry I missed that part...

Original Question : A Drum in the shape of a right circular cylinder is required to have a volume of 5000 cubic centimeters. The top and bottom are made of material that costs 5 cents per square centimeter, the sides are made of material that cost 4 cents per sq centimeters. (Hint: The formula for the volume of a right circular cylinder is V=Pie r^2 h, where r is the radius of the circular base and h is the height of the cylinder. The surface are of the sides can be determined by cutting the cylinderical shell vertically and flattening it out to get a rectangle whose dimensions can be determined.)

a) Express the total cost C of the material as a function of the radius r of the cylinder.
b) What is the cost if the radius is 25 cm?
c) Graph C=C(r). Using the graph, for what value of r, approximately, is the cost C least?

Sol : C = 4 ( 2pie r h ) + 5 (2pie r ^ 2 )
C(r) = 4 ( 2pie r ( 2 pie r/sroot 3 )) + 5 ( 2pie r^ 2)

2pie r / h = sq root 3 / 1


that's all I soved so far...I am lost, please help !!

thanks for ur help

 

[stapel]

The total volume is given by:

. . . . .V = (pi)r²h

(Note: The Greek letter is "pi"; "pie" is something one eats.)

Since the volume is given as being fixed at 5000 cubic units, then:

. . . . .5000 = (pi)r²

. . . . .5000/(pi) = r²h

. . . . .5000/[(pi)r²] = h

a) You have a good "cost" formulation. Now use the volume information to substitute for "h". This will leave you with a cost formula in terms only of the variable "r".

b) Plug in "25" for "r". Simplify.

c) I'm guessing they're wanting you to do a "trace" on your graphing calculator. So look at the graph, and zoom in on the lowest part. Find the approximate x-value (since "x" is standing in for "r" in the calculator's "graph" utility) that corresponds to the lowest spot on the graph.

Eliz.