« ΠροηγούμενηΣυνέχεια »
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?
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 ?
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.
A solid 2 units long, 1 unit wide, and 1 unit high contains 2 cubic units.
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. If we suppose the figure in the margin to represent a solid 5 ft.
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 ?
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
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
2-inch cubes can be covered with a sheet of paper 2 ft. square ?
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 ?