SOLUTION: the surface area of a right circular cylinder with a circular radius r and a height h is given by s= 2 pie r squared. explain why his is so. then find how much cardboard is needed

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Question 316753: the surface area of a right circular cylinder with a circular radius r and a height h is given by s= 2 pie r squared. explain why his is so. then find how much cardboard is needed to make a toilet paper tube if the tube is 4.5 inches long with a radius of 1 inch
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine a cardboard tube.
Cut the tube lengthwise and unroll it.
The tube is now unrolled and flattened into a rectangle.
The length of the rectangle is h along the cut line, L=h.
The width of the rectangle is the circumference of the circle or C=2%2Api%2AR.
The area of the rectangle is
A=L%2AW=h%2A2%2Api%2AR=2%2Api%2ARh
Your surface area formula would only be correct if h=R
R=1
h=4.5
A=2%2Api%2ARh=2%2Api%2A1%2A4.5
A=9%2Api sq.in. or approximately,
A=28.3 sq.in.