SOLUTION: Hi A rectangular piece of sheet metal with an area of 800 in^2 is to be bent into a cylindrical length of stovepipe having a volume of 400 in^3. What are the dimensions of the s

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Question 200166: Hi
A rectangular piece of sheet metal with an area of 800 in^2 is to be bent into a cylindrical length of stovepipe having a volume of 400 in^3. What are the dimensions of the sheet metal?
thanks for the homework help!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular piece of sheet metal with an area of 800 in^2 is to be bent
into a cylindrical length of stovepipe having a volume of 400 in^3.
What are the dimensions of the sheet metal?
:
Label the rectangular piece of metal as follows:
;
Let h = the length, (will be the length of the pipe)
Let c = the width, (will be the circumference of the pipe
:
The area of the metal
h * c = 800
h = 800%2Fc
:
Find the radius from the circumference
2*pi*r = c
r = c%2F%282pi%29
:
The volume:
pi*r^2*h = 400
:
Substitute (c/2pi) for r, and (800/c) for h
pi*c%2F%282pi%29*c%2F%282pi%29*800%2Fc%29 = 400
cancel out a pi and a c
c%2F2*1%2F%282pi%29*800 = 400
:
c%2F%284pi%29*800 = 400
Cancel the 4 into 800
%28200c%29%2Fpi = 400
:
200c = 400*pi
;
divide 200 into both sides
c = 2*pi
:
c = 6.283 is the circumference of the pipe
;
Find the height
h = 800%2Fc
h = 800%2F6.283
h = 127.33" is the height of the pipe
:
The dimensions of the metal: 127.33" by 6.283"
:
:
Check solution by finding the volume with these value
Find r
r = c%2F%282pi%29
r = 6.283%2F%282pi%29
r = 1"
:
V = pi*1^2*127.33
V = 400.0 cu/in