Problem 16
Each of mammoth dredges used in digging the Panama Canal had a dipper the capacity of which was 15 cu. yd. If the height of the dipper was 10 ft. 9½ in., what was the area of the bottom?
Problem 15
A spherical shell 2 in. thick has an outer diameter of 12 in. Find the volume of the material of which it is made.
Problem 14
A concrete surge chamber with circular cross section and vertical inner walls has an inside diameter of 100 ft. The outer walls taper uniformly. The outer walls taper uniformly ¼ in. to 1 ft. of rise, and at the base the thickness is 5 ft. The height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 150 lb. per cu. ft. Find the total weight of the chamber when full of water.
Problem 13
The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.
Problem 12
The water supply of a district consists of a lake whose surface area is 1000 acres. The number of household supplied with water is 60,000. Supposing each household to use 25 gal. per day, calculate how many days’ supply (to the nearest day below the exact number) is represented by a depth of 1 ft. of water in the lake. (1 acre equals 43,560 sq. ft.)
Problem 11
Find the waste in cutting the strongest square timber from a circular log of uniform diameter 2 ft. and length 8 ft.
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 9
An anchor ring is formed by revolving a circle 2 in. in diameter about a line lying in the plane of the circle and at a distance of 7 in. from its center. Find the volume of the solid formed.
Solution 9
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?
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