Making a Stovepipe A rectangular piece of sheet metal with an area of 1200 in2 is to be bent into a cylindrical length of stovepipe having a volume of 600 in3. What are the dimensions of the sheet metal?
The dimensions of rectangular piece of sheet metal.
Answer to Problem 46E
The dimensions of given sheet metal is 6.28 by 191.08 in.
Explanation of Solution
Given:
Area of rectangle piece of sheet metal is
Figure of sheet metal and cylinder is,
Figure (1)
Calculation:
Formula of area of rectangle is,
Dimensions of cylindrical length of stovepipe is shows in Figure (2),
Figure (2)
In the Figure (2) x is y are length and width of the metal sheet, when metal sheet bent into a cylinder y becomes height of cylinder and x is perimeter of surface circle of cylinder, gives the equation of perimeter of circle,
Solve the above equation to get value of radius of circle in x term,
Formula of volume of cylindrical stovepipe is,
Substitute
Substitute 3.14 for
Substitute
Substitute 6.28 for x in equation (1) to get the value of y,
Thus, the dimensions of given sheet metal is 6.28 by 191.08 in.
Chapter 10 Solutions
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