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Math problem when a cirlcle of radius 10cm is squeezed between two parallel lines 10cm apart, its area changes but its perimeter remains constant. waht fraction of the old area is the new area if the ends are semicircle?

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This sounds like someones homework. I'm risking my reputation here but here goes.

Previous Area was Pi x R x R. = Pi X 10 X 10 = 100 X Pi
Previous Perimeter is 2 X Pi X R = 2 X Pi X 10 = 20 X Pi

New shape is a rectangle with a semicircle at each end and width of 10 cm.
New Perimeter is circular bits + straight edges between them.
We know the circular bits but not how long the straight bits are so ...
Perimeter = 20 X Pi = (2 X Pi X 5) + L X 2 = 10 X Pi + (L X 2)
So L = (20 - 10) X Pi / 2 = 5 X Pi.

So the new Area is ... (Pi X 5 X 5) + (10 X 5 X Pi)
= 75 X Pi.
= 75 X 3.14 = 235.5

Posted on Nov 10, 2007

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