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Going Around in Circles
The geocache is found at N 49 AB.CDE W 097 W.XYZ. You will need to solve the following problems each involving π.
For NORTH:
1. Given that 2π radians is a full circle, find the number of degrees for an angle of 0.872664626 radians and divide this by 10 to get A.
2. In math East is taken as 0, north is 90 degrees or π/2 radians, west is 180 degrees or π radians, etc. Find the angle, in degrees, for 314 π radians. Divide your answer by 15. This angle is B.
3. A pizza π has a circumference of 56.55 inches. What is the radius of this pizza π? The radius is C.
4. Besides quilting, QuiltinAnnie likes making π for our sons-in-law: strawberry rhubarb in one case and apple in the other. Mr. QuiltinAnnie enjoys any π he can get. One of her πs has a surface of 113.1 units. What is radius of this π? The radius is D.
5. A giant spherical tank needs to be painted. The painter will eat π at break time. Each can of paint covers 500 square feet. The tank has a radius of 15 feet. What minimum number of cans of paint are needed to cover the tank once with less than one can of paint left over? The number of cans is E.
For WEST:
6. A cone has a volume of 209.44 cubic units. The radius of the base is 5 units. Find the height of the cone. The height is W. A cone makes one think of ice cream which is good to have on π.
7. A cylindrical cake is 4 inches tall. It has a total area to receive icing of 204 square inches. Only the top and sides get icing but not the bottom unless you really like icing but that would make serving difficult. When you don't have π then cake is a good second choice. What is the radius of the cake to the nearest inch. The radius is X.
8. An internal combustion engine has a total displacement of 2.7 L. Each cylinder has a diameter of 8.46 cm and a stroke length of 8.0 cm. How many cylinders does the engine have. This gives Y. These cylinders will be used to deliver the π made by QuiltinAnnie.
9. What is the 1,000,000th DIGIT of π? 3 is the first one. This digit is Z. If you get Z = 1 you are in error.