(5) How many cubic inches will there be in a log of wood 1 ft. 3 in. deep, the area of the bottom being 4 sq. ft. 62 sq. in.? (6) How many cubic feet of wood are there in a plank 16 ft. long, 10 in. broad, and 1 in. thick? (7) A pit 12 ft. square is 100 yds. deep; what did it cost to sink it, at 1s. 3d. per cubic yard? (8) A tank is 15 ft. long, 9 ft. wide, and 2 ft. deep; how many cubic feet of water will it hold? (9) A cistern is 5 ft. 4 in. long, 2 ft. broad, and 1 ft. 6 in. deep; what weight of water will it contain? (Express the result in cwts., qrs., lbs.) [A cubic foot of water weighs 1000 oz.] (10) A reservoir is 23 ft. 1 in. long, 12 ft. 6 in. wide, and 6 ft. deep; how many gallons will it hold? [A gallon of water contains 277 c. in.] (11) How many three-inch cubes can be cut out of a rectangular solid 4 ft. long, 2 ft. broad, and 1 ft. thick? [Compare Art. 42. Vol. of cube=3x3x3=27 c. in. Vol. of solid= 48 x 24 x 12-13824 c. in. No. of cubes in solid=13824÷27.] (12) Find how many bricks will be required to build a garden wall 60 ft. long, 18 in. thick, and 6 ft. high; a brick being 9 in. long, 4 in. wide, and 3 in. deep. (13) How many books 8 in. long, 4 in. broad, and in. thick, may be packed in a box 2 ft. 8 in. long, 1 ft. 8 in. wide, and 1 ft. deep? (14) A box, open at the top, 4 ft. long, ft. broad, and 2 ft. deep, is made of deal an inch thick; required the number of cubic feet and inches of wood in it. [First find the content of a solid with the external dimensions, and then subtract from this the content of the interior part of the box. Compare Art. 17. The external dimensions in inches are 48, 36, and 24; the internal dimensions are, length, 48-2, breadth 36-2, and depth 21-1.] (15) A box without a lid is made of wood 3 in. thick; its internal dimensions are 2 ft. 9 in., 2 ft. 3 in., and 1 ft. 9 in.; find the number of cubic feet and inches of the material. [In this case, to obtain the external dimensions, twice the thickness of the wood must be added to the length and breadth internally, and once only to the depth.] (16) In laying the foundation of a house, an excavation 24 ft. long, 18 ft. broad, and 12 ft. deep is made to form a cellar-kitchen. The thickness of the wall is 18 in.; how many cubic feet of air will the kitchen contain (17) A reservoir is 48 ft. long and 30 ft. broad; how many cubic feet of water must be drawn off to make the surface sink 2 ft.? [The volume of the water drawn off will be that of a rectangular parallelopiped, 48 ft. long, 30 ft. broad, and 2 ft. deep.] (18) What is the length of the edge of a cubical cistern which contains as much water as a rectangular one whose edges are 154 ft. 11 in., 70 ft. 7 in., and 53 ft. 1 in. ? (19) Find the difference in cost of materials between paving a street 90 yds. long and 21 ft. broad with cubical wooden blocks each of whose edges measures 9 in., and laying down asphalte 4 in. deep; the wooden blocks costing 9d. per dozen, and the asphalte 4d. per cubic foot? 144. To find one dimension when the volume and the other two dimensions are given. RULE. Divide the volume by the product of the two given dimensions, and the quotient will be the dimension required. Since length x bread depth = volume, [The volume and the known dimensions must be expressed in corresponding denominations.] Ex. 1. What length must be cut off a straight plank 9 in. wide and 2 in. thick, in order that it may contain a cubic foot? Ex. 2. A rectangular parallelopiped contains 132 c. ft.; its length and thickness are 11 ft. and 3 ft. respectively; required its breadth. Breadth = 132 = 4 ft. (5) How many cubic inches will there be in a log of wood 1 ft. 3 in. deep, the area of the bottom being 4 sq. ft. 62 sq. in.? (6) How many cubic feet of wood are there in a plank 16 ft. long, 10 in. broad, and 1 in. thick? (7) A pit 12 ft. square is 100 yds. deep; what did it cost to sink it, at 1s. 3d. per cubic yard? (8) A tank is 15 ft. long, 9 ft. wide, and 2 ft. deep; how many cubic feet of water will it hold? (9) A cistern is 5 ft. 4 in. long, 2 ft. broad, and 1 ft. 6 in. deep; what weight of water will it contain? result in cwts., qrs., lbs.) [A cubic foot of water weighs 1000 oz.] (Express the (10) A reservoir is 23 ft. 1 in. long, 12 ft. 6 in. wide, and 6 ft. deep; how many gallons will it hold? [A gallon of water contains 277 c. in.] (11) How many three-inch cubes can be cut out of a rectangular solid 4 ft. long, 2 ft. broad, and 1 ft. thick? [Compare Art. 42. Vol. of cube=3x3x3=27 c. in. Vol. of solid= 49 x 24 x 12=13824 c. in. No. of cubes in solid=13824÷27.] (12) Find how many bricks will be required to build a garden wall 60 ft. long, 18 in. thick, and 6 ft. high; a brick being 9 in. long, 4 in. wide, and 3 in. deep. (13) How many books 8 in. long, 4 in. broad, and in. thick, may be packed in a box 2 ft. 8 in. long, 1 ft. 8 in. wide, and 1 ft. deep? (14) A box, open at the top, 4 ft. long, 3 ft. broad, and 2 ft. deep, is made of deal an inch thick; required the number of cubic feet and inches of wood in it. [First find the content of a solid with the external dimensions, and then subtract from this the content of the interior part of the box. Compare T are 48, 36, and 24; the internal 3-2, and depth 24-1.] le of wood 3 in. thick; its 2 ft. 3 in., and 1 ft. 9 in.; nches of the material. al dimensions, twice the thickness e length and breadth internally, and is 18 in.; how (17) A reservoir is 48 ft. long and 30 ft. broad; how many cubic feet of water must be drawn off to make the surface sink 2 ft.? [The volume of the water drawn off will be that of a rectangular parallelopiped, 48 ft. long, 30 ft. broad, and 2 ft. deep.] (18) What is the length of the edge of a cubical cistern which contains as much water as a rectangular one whose edges are 154 ft. 11 in., 70 ft. 7 in., and 53 ft. 1 in. ? (19) Find the difference in cost of materials between paving a street 90 yds. long and 21 ft. broad with cubical wooden blocks each of whose edges measures 9 in., and laying down asphalte 4 in. deep; the wooden blocks costing 9d. per dozen, and the asphalte 4d. per cubic foot? 144. To find one dimension when the volume and the other two dimensions are given. RULE. Divide the volume by the product of the two given dimensions, and the quotient will be the dimension required. Since length × bread ✩ × depth = volume, [The volume and the known dimensions must be expressed in corresponding denominations.] Ex. 1. What length must be cut off a straight plank 9 in. wide and 2 in. thick, in order that it may contain a cubic foot? Ex. 2. A rectangular parallelopiped contains 132 c. ft.; its length and thickness are 11 ft. and 3 ft. respectively; required its breadth. 132 = 4 ft. (5) How many cubic inches will there be in a log of wood 1 ft. 3 in. deep, the area of the bottom being 4 sq. ft. 62 sq. in.? (6) How many cubic feet of wood are there in a plank 16 ft. long, 10 in. broad, and 14 in. thick? (7) A pit 12 ft. square is 100 yds. deep; what did it cost to sink it, at 1s. 3d. per cubic yard? (8) A tank is 15 ft. long, 9 ft. wide, and 2 ft. deep; how many cubic feet of water will it hold? (9) A cistern is 5 ft. 4 in. long, 2 ft. broad, and 1 ft. 6 in. deep; what weight of water will it contain? (Express the result in cwts., qrs., lbs.) [A cubic foot of water weighs 1000 oz.] (10) A reservoir is 23 ft. 1 in. long, 12 ft. 6 in. wide, and 6 ft. deep; how many gallons will it hold? [A gallon of water contains 277 c. in.] (11) How many three-inch cubes can be cut out of a rectangular solid 4 ft. long, 2 ft. broad, and 1 ft. thick? [Compare Art. 42. Vol. of cube=3x3x3=27 c. in. Vol. of solid= 49x24x12=13824 c. in. No. of cubes in solid=13824÷27.] (12) Find how many bricks will be required to build a garden wall 60 ft. long, 18 in. thick, and 6 ft. high; a brick being 9 in. long, 4 in. wide, and 3 in. deep. (13) How many books 8 in. long, 4 in. broad, and in. thick, may be packed in a box 2 ft. 8 in. long, 1 ft. 8 in. wide, and 1 ft. deep? (14) A box, open at the top, 4 ft. long, 3 ft. broad, and 2 ft. deep, is made of deal an inch thick; required the number of cubic feet and inches of wood in it. [First find the content of a solid with the external dimensions, and then subtract from this the content of the interior part of the box. Compare Art. 17. The external dimensions in inches are 48, 36, and 24; the internal dimensions are, length, 48-2, breadth 36-2, and depth 21-1.] (15) A box without a lid is made of wood 3 in. thick; its internal dimensions are 2 ft. 9 in., 2 ft. 3 in., and 1 ft. 9 in.; find the number of cubic feet and inches of the material. [In this case, to obtain the external dimensions, twice the thickness of the wood must be added to the length and breadth internally, and once only to the depth.] (16) In laying the foundation of a house, an excavation 24 ft. long, 18 ft. broad, and 12 ft. deep is made to form a cellar-kitchen. The thickness of the wall is 18 in.; how many cubic feet of air will the kitchen contain |