Question 1789
these sorts of questions are lovely questions (yes, i guess i must be a sad individual)...anyway, draw a rectangle, vertical side a and horizontal side b

the area = ab = 1200

Now draw an upright cylinder (by wrapping the length b into a circle)...its radius is length r, and its height is a

Volume of this cyclinder is the area of the circular end times the height...

{{{volume = pi*r^2*a}}}

now, seeing as how i do not know what r is, i had better find it. This is found from the circumference of the circle (which is the length b)...

circumference, b = {{{2*pi*r}}}

so, {{{r = b/(2*pi)}}}

So, we can get rid of the r in the volume equation..this is now re-written as:

{{{volume = pi* (b/2*pi)^2 * a}}}
{{{volume = (pi*a*b^2)/(4*(pi)^2)}}}. This can be simplified to

{{{volume = (a*b^2)/(4*pi)}}}

So we know the volume, but not a or b...2 unknowns in 1 equation is NOT good, so we need to get rid of either a or b...we do this by using the area equation, at the start of this explanation...let's re-write it as a = 1200/b

so we now get {{{volume = (1200b^2)/(4*b*pi)}}}

cancel the b with one of those in the {{{b^2}}} term, and simplifying the 1200 and 4 gives

{{{volume = (300b)/(pi)}}}

{{{600 = 300b/pi}}}

so, {{{b = (600pi)/(300)}}} --> b=2pi

Substitute this into the area equation and you find a=600/pi. These are the dimensions of the sheet metal.

cheers
Jon.