3. Find the circumference of a circle whose diameter is 42 feet. Find the area. 4. A horse is tied to a tree by a rope 20 ft. long. Over what area can he pasture ? 5. What is the area of a circle whose circumference is 1 of a mile ? 1. How many sides, or faces, has the cube? Of what shape are they? How do the six faces compare in size ? 2. How many edges has the cube? How many corners ? 3. How many edges bound each face ? Does each edge form a part of the boundary of more than one face ? If so, of how many faces ? 4. How many corners has each face of the cube? 5. How many faces of a cube are parallel to any one face ? How many edges are parallel to any one edge ? The figure above represents a cubic inch. A cubic inch is a cube each of whose edges is one inch long. For definition of cube, see p. 108. 6. How high is a cubic foot ? How wide? How long ? 7. Define a cubic foot. 8. Define a cubic yard. 9. What is the area of a cubic inch ? 10. What is the area of a cube each of whose edges is 2 in. long ? 11. What is the area of a cube each of whose edges is 4 in. long? How many A solid bounded by six rectangular faces is called a Rectangular Solid. 12. How many edges has this figure ? corners ? 13. In what particular respect does the above figure resemble the cube? In what respect does it differ from the cube? 14. If the above figure is 4 in. long, 2 in. high, and 2 in. wide, what is the area of one end ? Both ends ? What is the area of one side ? Of the four sides? What is the total area ? SOLIDS LESSON 119 The Volume of a solid is the number of cubic units which it contains. The principal English cubic units are the cubic inch, cubic foot, and the cubic yard. A solid 1 unit long, 1 unit wide, and 1 unit high contains 1 cubic unit. А A solid 2 units long, 1 unit wide, and 1 unit high contains 2 cubic units. B В 1. Considering A a cubic foot, what is the volume of D? Of E? 2. If A is a cubic yard, what is the volume of D? How many cubic yards are there in one layer of E? In both layers ? 3 2 2 3 ft. 3. If we suppose the figure in the margin to represent a solid 5 ft. 1 3 4 / 5 long, 3 ft. wide, and 4 ft. high, what is the cubic unit of measure ? 4. Count the number of cubic feet in the top layer. How many are there? 5 ft. 5. Can you say that the top layer has 5 rows with 3 cubic feet in each row ? 6. Is it also true that it has 3 rows with 5 cubic feet in each row ? 7. The height is 4 feet. How many layers of cubic feet, therefore, are there in the height? 8. What is the total number of cubic feet in the volume of the figure ? 9. Can you give a rule for calculating the volume of a solid when you know the three dimensions ? LESSON 120 1. How many cubic inches are there in a brick 8 in. long, 4 in. wide, and 2 in. thick ? 2. How many cubic inches are there in a solid 5 ft. long, 4 ft. wide, and 2 ft. thick ? 3. How many cubic feet are there in a cube each edge of which is 3 ft. ? What is the name of such a cube? 4. How many cubic inches of sand will a box hold that is 5 in. long, 4 in. wide, and 3] in. deep ? 5. How many cubic inches are there in a solid 5 ft. square at the base, and 3 ft. high? 6. What is the volume of a cube whose edge is 5 in. ? 7. How many cubic inches can be cut from a cube whose edge is 4 in. ? 8. How many cubic feet are there in a solid 4 ft. long, 3 ft. wide, and 24 ft. high? 9. How many square feet of paper will be needed to cover a cube whose edge is 3 ft. ? 10. If the cube mentioned in the preceding question be cut into cubic feet, would it require the same amount of paper to cover the smaller cubes ? If not, how much more paper would be needed in the one case than in the other? 11. How many 1-inch cubes can be covered with a sheet of paper 12 in. square ? 12. How many 2-inch cubes can be covered with a sheet of paper 2 ft. square ? LESSON 121 1. Which will hold the more, 2 boxes each 14 in. long, 10 in. wide, and 6 in. deep, or 4 boxes each 7 in. long, 5 in. wide, and 3 in. deep ? 2. How many cubic feet and cubic inches are there in 3990 cu. in. ? 3. How many cubic yards and cubic feet in 800 cu. ft. ? 4. There are 231 cu. in. in a gallon. How many gallons will a tin box hold that is 11 in. long, 7 in. wide, and 3 in. deep ? 5. How many gallons will a box hold that is 22 in. long, 14 in. wide, and 6 in. deep 6. How many bricks 8 in. x 4 in. x 2 in. would be needed for a wall 10 ft. long, 6 ft. high, and 1 ft. thick ? |