A rectangular sheet metal w/ an area of 1200 in虏 is bent into a cylinder w/ volume of 600 in鲁. Dimensions?

We are looking for the dimensions of the original rectangular sheet metal, not the new cylindrical ';stovepipe';. Please show work so that I will know how to solve this problem.





I ALWAYS select the best answer. Thank you.A rectangular sheet metal w/ an area of 1200 in虏 is bent into a cylinder w/ volume of 600 in鲁. Dimensions?
The rectangle:


A = b * h


When the rectangle is bent into a cylinder, the base b will become the circumference, while the height of the rectangle will be the height of the cylinder.


b = 2 pi r


r = b / (2pi)


V = pi r^2 h = pi h (b / (2pi))^2 = pi*h*b^2 / 4 pi^2 = h*b^2 / 4 pi


1200 = (b * h)


600 = h*b^2 / 4 pi


600 = b * (b * h) / 4 pi


600 = b * (1200) / 4 pi


b = 2 pi


Since A = b * h, h = 600 / pi





Thus, the dimensions are 2 pi meters x 600/pi metersA rectangular sheet metal w/ an area of 1200 in虏 is bent into a cylinder w/ volume of 600 in鲁. Dimensions?
V=pi(r^2)h=600





A=lw=1200 which is when h=l and w=Circumference of the pipe...





Circumference of the pipe is 2(pi)r so 2(pi)(r)h=1200 and pi(r)(r)h=600 set the equations to each other.....





1200=2pi*r*r*h=2pi*r*h





using the last two parts of the above equation you should be able to cancel out (on both sides) a 2pi(r)h term....thus finding r=1





if r=1 then you can use the fact that w=2(pi)r , A=1200, and that A=wl....





w=2pi, and so l=600/pi