math
posted by Yuni .
the volume of an cylindrical can with a radius r cm and height h cm is 128000 c^3, show that the surface area of the can is A=2(22/7)r^2 + 246000/r. Find the value for r to minimize the surface area.
*i know what the quest. ask but i do not know how to apply it.

It looks like you are being asked to use 22/7 for pi. In that case,
2(22/7)r^2 is the combined area of the two circular ends.
If the volume is V = pi*r^2*h, the curved cylindrical area is
2 pi*r*h = 2V/r.
That is where your 246000/r term comes from.
To minimize the surface area, set the derivative of A(r) equal to zero.
dA/dr = (88/7) r 246,000/r^2 = 0
r = (246,000*7/88)^1/3 = 26.9 cm
If you have not yet studied differential calculus, I suggest you graph A vs r and see where it is a mininum.
Respond to this Question
Similar Questions

Math  Geometry
A cylindrical solid has a cylindrical circular hold drilled out of the center. Bascially, it's a circular cylinder with a hollow spot right down the middle. Find the surface area of the resulting solid. radius of larger circle: 2in … 
mathPLEASE CHECK AND HELP
find the surface area and volume of the right circular cylinder. The radius is 3 and height 6. This is what I put for volume: v=pir^2h pi(3cm)^2 6 cm= 54pi cm cubed can you please check this and show work on how to do the surface area? 
Math 11 Surface area, Volume and Capacity
A cylindrical tin can has a radius of 4.5cm and a height of 5 cm (a)What is the surface area of the can (b)What is its volume? 
math
If the volume of a cylindrical block is equal to 800cm^3 prove that the total surface area is equal to 2(pi)x^2 + (1600)/x, where x cm is the radius of the base. hence obtain the value x which makes the surface area a minimum. 
Math
Optimization Problem A right circular cylindrical can of volume 128tπ cm^3 is to be manufactured by a company to store their newest kind of soup. They want to minimize the surface area of the can to keep costs down. What are the … 
math
find the radius and height of a cylindrical soda can with a volume of 21in^3 that minimize the surface area. 
Calculus
A company needs to make a cylindrical can that can hold precisely 1.5 liters of liquid. If the entire can is to be made out of the same material, find the dimensions (radius and height) of the can that will minimize the cost. Round … 
MATH
If the volume of a cylindrical block is equal to 800cm^3 prove that the total surface area is equal to 2(pi)x^2 + (1600)/x, where x cm is the radius of the base. hence obtain the value x which makes the surface area a minimum 
math
3.A rectangular prism has a width of 92ft and a volume of 240ft.Find the volume of a similar prism with a width of 23ft.Round to the nearest tenth, if necessary. 4.A pyramid a height of 5in. and a surface area of 90in^2.Find the surface … 
Math
A manufacturing company wants to minimize the cost of materials for a pop can which needs to hold 640 mL. Find the radius and height (in centimeters) of the cylindrical can with minimum surface area that holds this volume. Give your …