MATHalino

Problem 27
One hundred and fifty posts are used in fencing a lawn. Each post is built in the form of frustum of a pyramid surmounted by a pyramid whose lower base is common with the upper base of the frustum. The height of the pyramidal top is 2 in. and the common base is a square 4 in. on an edge. The lower base of the frustum has an edge of 6 in. If the overall height of each is 6 ft., how much concrete will be used in making the posts?
 

Problem 26
A wooden ball 2 ft. in diameter weighs 200 lb. Find the diameter of a ball of the same material which weighs 50 lb.
 

Problem 25
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.)
 

Problem 24
A pipe of 3/4-in. inside diameter conducts water from a spring to a house 300 ft. distant. It is desired to empty the pipe after the water has been turned off the spring. Will a 10-qt. pail hold the water? (One gal. = 231 cu. in.)
 

Problem 23
It is desired to cut off a piece of lead pipe 2 in. in outside diameter and 1/4 in. thick, so that it will melt into a cube of edge 4 in. How long a piece will be required?
 

Problem 22
How many square feet of tin are required to make a funnel, if the diameters of the top and bottom are 28 in. and 14 in., respectively, and the height is 24 in.?
 

Problem 21
A stone is dropped into a circular tub 40 in. in diameter, causing the water therein to rise 20 in. What is the volume of the stone?
 

Problem 20
A factory chimney has the shape of a frustum of a regular pyramid. Its height is 180 ft., and its upper and lower bases are squares whose sides are 10 ft. and 16 ft., respectively. The cross section of the flue is a square whose side is 7 ft. How many cubic feet of material does the chimney contain?
 

Problem 19
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?
 

Problem 18
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.