Problem 39
A grain elevator in the form of a frustum of a right circular cone is 24 ft. high, and the radii of its bases are 10 ft. and 5 ft., respectively; how many bushels of wheat will it hold if 1-1/4 cu. ft. equals 1 bu.?
Problem 38
A log 18 ft. long is 2 ft. in diameter at the top end and 3 ft. in diameter at the butt end.
Hint: In (b) the larger end is the square ABCD. What is the smaller end? In (c) one end is the square EFGH. What is the other end?
Problem 37
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?
Problem 36
A hole 6 in. in diameter was bored through a sphere 10 in. in diameter. Find the volume of the part cut out.
Problem 35
In the foundation work of the Woolworth Building, a 55-story building in New York City, it was necessary, in order to reach the bedrock, to penetrate the sand and quicksand to a depth, in some instances, of 131 ft. If the largest circular caisson, 19 ft. in diameter, was 130 ft. deep and was filled with concrete to within 30 ft, of the surface, how many cubic yards of concrete were required?
The inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?
Problem 33
Disregarding quality, and considering oranges as spheres, determine which is the better bargain, oranges 2-3/4 in. in diameter at 15 cents per dozen, or oranges averaging 3-1/2 in. in diameter at 30 cents per dozen.
Problem 32
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.
