ASSIGNMENT - SOLIDS FOR WHICH V=BH
1. Atrenchis200ft.loegandl2ft.deep,Sft.wideatthetOPand4ft. wide at the bottom. How many cubic yards of earth have been removed?
2. When an irregular-shaped rock is placed in a cylindrical vessel of water whose radius is 4.l8~ in., the water rises 6.85 in. What is the volume of the
3. rock if it is completely submerged?
4. A dam is 40 ft. long, 12 ft. high, 7 ft. wide at the bottom, and 4 ft. wide at the top. How many cubic yards of material were used in constructing it?
5. L 4. Two rectangular water tanks with tops on the same level are connected
a. by a pipe through their bottoms. The base of one is 6 in. higher than that of
b. the other. Their dimensions are 4 by 5 by 2~ ft. and 4 by 7 by 3 ft., respec
6. r ~ tively. How deep is the water in the larger tank when the water they contain equals half their combined capacity, if the 2fft. and 3-ft. edges are vertical?
1. A cylindrical tin can holding 2 gal, has its height equal to the diameter of its base. Another cylindrical tin can with the same capacity has its height equal to twice the diameter of its base. Find the ratio of the amount of tin required for making the two cans with covers.
2. How much wood is wasted in turning out the largest possible cylindrical rod from a stick whose uniform square cross- sectional area is 10 sq. in. and whose length is 5 ft.?
3. How long a wire 0.1 in. in diameter can be drawn from a block of copper 2 by 4 by6 in.?
4. A piece of lead pipe is 50ft, long. Its outer radius is 2 in., and it is ~ in. thick. Into how many spherical bullets ~ in. in diameter can it be melted?
5. A corncrib 20 ft. long has a cross section ‘which is represented in the figure. The crib is entirely filled with corn on the ear. How many bushels bf corn does it contain, if 2 bu. of corn on the ear are equal to I. bu. of shelled corn? (Use the approximation,~1 bu. = 1~ Cu. ft.)
6. How many bricks each 8 in.~ by 2~ in. by 2 in. will be required to build a wall 22 ft. by 3 ft. by 2 ft. (not alkwing for mortar)?
7. The height of a hot-water boiler attached tG a furnace is 5~ ft. The circumference of the boiler is 48 in. If the metal is j in. thick, how many gallons will the boiler contain when full? (One gal. 231 cii. in.)
8. A cylindrical tank~ diameter 1 ft., length 6 ft., is placed so that it~áxis is horizontal. How many pounds of water will be used in filling it to ~depth of 9 in., if water weighs 62.4 lb. per cu. ft.?
9. How many washers can be made from a cube of metal 4 in. on a side, ii the washers are ~ in. in diameter and j in. thick? The hole in the center of the washers is ~ in. in diameter.
10. What are the dimensions of a gallon can of uniform square cross section whose height is twice the length of an edge of its base? (One gal. equals 231 cu. in.)
11. A wood in an makes a wedge-shaped cut in the trunk of a tree. Assume that the trunk is a right circular cylinder of radius 4 in., that the lower surface of the cut is a horizontal plane, and that the upper surface is a plane inclined at an angle of 450 to the'horizontal and intersecting the lower surface of the out in a ‘diameter. This wedge is then cut into two equal pieces by a vertical cut. What is the area of this vertical section? The woodnian now wishes to divide one of these pieces by another section 4. parallel to the first section. If the new section is to have an area equal to one-fourth that of the original section, where should the cut be made?
12. How deep a cut should be milled off one side of a 2k-in. shaft to make a flat (a rectangular flat area) i~ in. wide?
13. The base of a right cylinder is shown in the figure. it is formed by describing semicircular arcs within the square upon the four sides as diani-eters. If the altitude of the cylinder is 12 in., find the volume and total area.