Problem 10
How many cubic inches of lumber does a stick contain if it is 4 in. by 4 in. at one end, 2 in. by 2 in. at the other end, and 16 ft. long?
 

Problem 8
Find the diameter of the base of the pint tin can whose height is 4 in. (231 cu. in. = 1 gal.); also, find the number of square feet of tin required to manufacture 10,000 such cans with tops. (Neglect the waste due to seams, etc.)
 

Problem 7
If a piece of brass 8 by 6 by 12 in. is drawn out into a wire 1/30 in. in diameter, what will be the length of the wire?
 

Problem 6
A light is placed 5 ft. from the center of the globe 3 ft. in diameter. Find the area of the illuminated portion.
 

Problem 5
If the gravity whose cross section is shown in the figure weighs 150 lb. per cu. ft., find the total weight of a section of a dam 50 ft. long.
 

Problem 4
In Fingal’s Cave, on the Island of Staffa (Hebrides, Scotland), the walls are formed by basaltic prismatic columns varying in height from 18 to 36 ft. These columns, mostly hexagonal, are so perfect as to suggest the hand of man. One of the vertical columns is 29.3 ft. in height and has a base of 4.7 sq. ft. What is its volume?
 

Problem 3
Two spheres of lead, of radii 2 and 3 in., respectively, are melted into a cylinder of revolution of radius 1 in. Find the altitude of the cylinder.
 

Problem 2
The great Chinese wall is said to be 1500 miles long, 20 ft. high, 15 ft wide at the top, and 25 ft. wide at the bottom. If it were possible to build with this material a wall around the earth at the equator, of a uniform thickness of 4 ft., how high could it be made? (The equator is approximately 24,900 miles long.)
 

Problem 1
Find the weight of a brass water pipe 20 ft. long whose inside diameter is 1.5 in. and whose thickness is 1/4 in., if brass weighs 520 lb. per cu. ft.