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?
cylinder V = 蟺r虏h


600 in鲁 = 蟺r虏h


cylinder side area = circumference x h = 蟺dh = 2蟺rh


1200 in虏 = 2蟺rh


600 in虏 = 蟺rh





2 equations 2 unknowns


蟺r虏h = 600


蟺rh = 600


h = 600/蟺r





蟺r虏(600/蟺r) = 600


lots of things cancel


r = 1 inch


h = 600/蟺r = 600/蟺 = 191 inch





check


V = 蟺r虏h = 蟺1虏191 = 600


A = 2蟺rh = 2蟺191*1 = 1200





.A rectangular sheet metal w/ an area of 1200 in虏 is bent into a cylinder w/ volume of 600 in鲁. Dimensions?
Let's call the sides of the sheet a and b.


When you bend it to a cylinder, a will make up the height of the cylinder, whereas b will be the circumference of the ';ground floor';.





Information given is therefore:


a * b = 1200


b虏 * [pi] / 2 * a = 600





Try ro solve it like this:


a = 1200 / b -%26gt; substitute a with b


b虏 * [pi] /2 * 1200/b = 600


b虏 * [pi] * 1200/b = 1200


b * [pi] * 1200 = 1200


b = 1200 / 1200*[pi]


b = 3,142





a = 1200/b = 1200/3,142 = 381,971





To check if its correct:





a * b* = 3,142 * 381,971 = 1200








Hope I didn't make any mistakes ;)
volume of cylinder = pi()*r^2*h/4 = 600





rectangle one edge = height, other edge = circumference





area of rectangle = 2*pi()*r*h = 1200


h = 1200/(2*pi()*r)





from volume eqn. h = (600*4)/(pi()*r^2





so (2400)/pi()r^2 = 600/(pi()*r


or 4/r^2 = 1/r


or 4r = r^2


4 = r





h = 47.75





rectangle = 1200 = h*w, w = 1200/47.75 = 25.13





check, circumference = 2*pi()*r = 8*pi() = 25.13