Need size of a cylindrical can, able to contain 1/2 litre drink, maufactured from aluminum, volume is 500cm3?

Question

I'm desperate cuz this is needed to pass 8th grade! Please help me...

The teacher made us write a page that has radius/height/surface area/volume across the top, and I need a combo for the 20 (increasing) radius beginning with 0.5 and graduating to 10.0. The vol. 499.95-500.5. THANK YOU VERY MUCH!

Here are tips:

Need to find the radius and height of the can which will use the least aluminum,(ie: find out how to minimise the surface area of the can).
WHAT SHAPE IS YOUR CAN? DO YOU KNOW OF ANY CANS WITH THIS SHAPE?
Let the radius of the can be r cm, and the height be h cm. Write down algebraic expressions which give:
-the volume of the can
-the total surface area of the can, in terms of r and h. (Remember to include the two ends!)

Using the fact that the volume of the can must be 500 cm3, -you could either try to find some possible pairs of values for r and h (do this systematically if you can). -for each of your pairs, find out the corresponding surface area.

Answer 1

V=h*pi*r^2, h=V/(pi*r^2)
A = 2*pi*r^2 + 2*h*pi*r = 2(pi*r^2+V/r)
A=2V/h +2V/r = 2V(1/h+1/r)
Note: r & h are no longer independent variables if you fix V
From here on, it's guess-and-check.

good luck.

Answer 2

The can is cylindrical. The volume is pi*r^2*h The area of the can is the area of the bottom and top = 2*pi*r^2 plus the area of the sides which is the circumference of the ends times the height = 2*pi*r*h. So the surface area S = 2*pi*r^2 + 2*pi*r*h. You require the can to have a fixed volume V. So pi*r^2*h = V. Using the suggestion at the end of your question, plug in each radius value; calculate the resulting h from the volume formula, then using that h and r calculate the surface from the surface formula. You should have three colums of figures r, h, and S. You should be able then to fine where S is the lowest.

Answer 3

It's a cylinder which has a specified volume so you can work out height in terms of radius. So you can work out surface area in terms of radius. You need to find the value of r which minimises the surface area so the surface area will be bigger for larger r and will also be bigger for smaller r. So find r where dA/dr = 0 and check that for bigger and smaller r you get an increase in surface area.

I get volume ( for r and h in centimeters ) 500=h*pi*r^2 so h=500/pi/r^2

and surface area = 2*pi*r*h +2*pi*r^2 = 2*pi*r*(500/pi/r^2 + r)

=2*pi*(500/pi/r +r^2) - the 2*pi obviously doesn't matter so can you differentiate 500/pi/r + r^2 w.r.t. r then find the value of r for which this differential is zero?

Answer 4

the equation to use is :

Pi x R^2 x H = 500cm^3 (volume)

Answer 5

u should use a perfect sphere