St. Louis Science Center Planetarium Mathematics I.
Planetarium Playground Whisper Dishes
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. )
A Curve Fit To A Whisper Dish
Turn one of the whisper dishes to face upward. Then a parabola of the general type y = a x2 may be used to represent a cross section of the dish. Rotating this curve about the y axis may be close to carving the 3-D shape of the dish.
If the dish is 100 inches across and 15.375 inches deep then we can assume the vertex to be the point (0,0) and a point (50, 15.375) located on the rim. Let x = 50 and y = 15.375 then the value of a is found by substitution and simplifying. You may confirm that a = .00615.
Now establish the coordinates of the focus as (0, 40.65).
Take a yard stick on your next trip to the playground and check the distance from the vertex to the whisper ring in front.
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