What is the area of the largest possible Norman window with a perimeter of 32 feet? - norman window area
A Norman window has the shape of a crescent on a rectangle, so that the diameter of the semicircle corresponds to the width of the rectangle. What is the area of the window of the largest Norman possible, with a circumference of 32 feet?
Sunday, January 31, 2010
Norman Window Area What Is The Area Of The Largest Possible Norman Window With A Perimeter Of 32 Feet?
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1 comments:
Rys radio page you have:
Area = (pi * r ^ 2) / 2 + 2 R * S
Perimeter = (2pi * r) / 2 + 2 + 2 * s * r
So, if the volume = 32, then
32 = pi * r * s + 2 + 2 * r = (2 pi) r + 2s
or
n = 16 - r - (pi / 2) * r
Implement the area formula
Area = (pi * r ^ 2) / 2 + 2 * r (16 - r - (pi / 2) * r)
= (Pi * r ^ 2) / 2 + (32r - 2 r ^ 2 - (pi) * r ^ 2)
= R ^ 2 * [pi / 2 to 2 - pi] + 32r
R ^ 2 = [-2 - pi / 2] + 32r
The derivation of this
R [-4-pi] + 32
Is zero, there
[4 + pi] r = 32
r = 32 / [4 + pi] = 4.4808
n = 16 - r - (pi / 2) * r = 16 - (1 + pi / 2) * r = 16 to 2.5708 * 4.4808 = 4.4808 (surprise!)
Area = (pi * r ^ 2) / 2 + 2 R * S
= 3.1415927 * 4.4808 ^ 2 / 2 + 2 * 4.4808 * 4.4808
= 31.5378 + 40.1551 = 71.6929
Time: Squaring the Circle 32: Area = 64
Circle with a circumference of 32: Area = 81.4873
seems reasonable
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