Soap kettles used in the commercial manufacture of soap are as a rule large cylindrical vats, 50,000 lb. or more of soap being made in a single beating. Find the capacity of such a kettle having an inside diameter of 18 ft and an altitude of 30 ft. if soap weighs 70 lb. per cu. ft.
A factory chimney is in the form of frustum of regular square pyramid. The chimney is 125 ft. high the edges of its bases are 12 ft. and 8 ft., respectively. The cross-section of the flue is 6 ft. square. How many cubic feet of material does the chimney contain?
A coffee pot is 5 in. deep, 4-1/2 in. in diameter at the top, and 5-3/4 in. in diameter at the bottom. How many cups of coffee will it hold if 6 cups equal 1 quart? Answer to the nearest whole number.
A reservoir 10 ft. deep is in the form of a frustum of inverted square pyramid with bases of 100 and 90 ft. on a side respectively. How long will it require an inlet pipe to fill the reservoir if the water pours in at the rate of 200 gal. per min.? (One gal. = 231 cu. in.)
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.