December 2010

Example 013
Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.
 

Example 012
Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.
 

Example 011
A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single sphere resting on top. If the bottom layer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres?
 

Example 010
An igloo or Eskimo hut is built in the form of a hemispherical shell with an inside diameter of 12 ft. If the igloo is constructed of snow block having a uniform thickness of 2 ft and weighing 40 lb/ft³, find the weight of the igloo, neglecting the entrance. Also, if fresh air contains 0.04% carbon dioxide, find the amount of this gas in the igloo when freshly ventilated.
 

Example 009
A store sells the same quality of oranges graded as to size. A grade of orange 2½-inch in diameter sells \$3.00 per dozen. What should be the cost of grade 2-inch in diameter?
 

Example 004
The surface of a hemispherical dome whose diameter is 10 m is to be covered with gold leaf which costs \$0.25 per square centimeter. What must be paid for the gold leaf?