St. Louis Science Center Planetarium Mathematics I. or II.
Level B Circumference And Floor Area
Outer Cylinder Lateral Surface Area
Name ____________________ Date __________
Solve the problem(s) stated below and attach any graph paper graphs or diagrams. Turn this in to your teacher for class interest. If you wish to email your work to the address below - please use your initials in place of your name. You will probably not get a return response other than a smile. For helpful suggestions link here. For resource equations or formulas related to the St. Louis Science Center Planetarium click here: 
Problem:
( Print this page to work and turn in. )
The outside window's base line of level B form a regular polygon of 72 sides. We consider this wall of windows, lateral surface, a cylinder in this problem. First consider the radius of this cylinder.
From the window calculations we can calculate the the distance from the window's midpoint, the apothem, to the center of the 72-gon.
a) Window cylinder radius used =
b) The formula for the circumference of a circle:
c) The calculation of the circumference of the window cylinder's base, floor, circle =
d) The formula for the area of a circle:
e) The calculation of the area of the window cylinder's base, floor, circle =
f) What is the formula for the lateral surface area of a cylinder if you know the radius of the base and the height of the cylinder?
g) Use calculus to rotate height about a center line to prove this formula. (Look up the formula if no calculus background.)
h) What is the lateral surface area of this cylinder if the cylinder height is 15.xxxxx feet?
h = __________ feet
Lateral Surface Area Of Cylinder = __________ square feet
Write "SLSCP Regular 72-gon Mathematics II. Problem(s)" based on these.
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