A druggist sells a certain kind of powder in a rectangular box 4 by 2 by 1 in. for 25 cents, and in a cylindrical can 2½ in. high and 2½ in. in diameter for 10 cents. Which is the more economical buy?
A stone bridge has three equal semicircular arches resting on four equal rectangular piers. The radius of each arch is R, the dimensions of the piers L, W, H, while the distance from the top of each pier to the top of the bridge is D. If L = 50 ft., W = 5 ft., H = 10 ft., R = 6 ft., D = 12 ft., find the number of cubic yards of material used in building the bridge.
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.
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.
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.)