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.

A

A solid 2 units long, 1 unit wide, and 1 unit high contains 2 cubic units.

A solid 3 units long, 1 unit wide, and 1 unit high contains 3 times 1, or 3 cubic units.

A solid 3 units long, 2 units wide, and 1 unit high contains 3 times 2, or 6 cubic D

units.

C

B

A solid 3 units long, 2 units wide, and 2 units high contains 3 × 2 × 2, or 12 cubic units.

If A is a cubic inch, the volume of B is

2 cu. in.; C is 3 cu. in., etc.

E

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?

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 21 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 31 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. × 4 in. × 2 in. would be needed for a wall 10 ft. long, 6 ft. high, and 1 ft. thick?

7. Find the volume of a solid 10 in. long, 6 in. wide, and 4 in. thick. How many square inches in its surface? The unit in Wood Measure is the cord.

8. A cord foot is what part of a cord? 9. How many cord feet make a cord?

10. How many cord feet are there in 32 cu. ft.? In 48 cu. ft. ?

11. 48 cu. ft. equal what part of a cord?

LESSON 122

1. How many cords are there in a pile of wood 24 ft. long, 12 ft. high, and 4 ft. wide?

The number of cubic feet in the

=

OPERATION

=

pile 24 x 12 x 4, or 1152. Divid- 24 x 12 x 4 1152 cu. ft. in pile. ing 1152 by 128, the number of

cubic feet in a cord, we get 9, the

number of cords.

1152128 = 9 cords.

2. How many cubic feet are there in a pile of wood 32 ft. long, 4 ft. wide, and 4 ft. high? How many cord feet? How many cords?

3. How many cords of wood are there in a pile 32 ft. long, 91 ft. high, and 4 ft. wide? How much is the wood worth at $4 a cord?

4. How many cords of wood can be put into a shed 24 ft. long, 16 ft. wide, and 12 ft. high? How much is the wood worth at $4.50 a cord?

5. Find the number of cubic yards of earth that will have to be removed in digging a cellar 24 ft. long, 18 ft. wide, and 6 ft. deep. What will be the cost at 30 a load (1 cu. yd.)?

The unit in Board Measure is the board foot. The board foot is a square foot one inch thick.

6. How many board feet are there in a piece of board 2 ft. long, 1 ft. wide, and 1 in. thick?

7. Find the number of board

1foot

Foot

+1 foot

feet in a board 15 ft. long, 16 in. wide, and 1 in. thick.

The shape of the board is that of a rectangle. To find the area of a rectangle we multiply the length by the width.

OPERATION

16÷121, width of board in ft. 1 × 15:

=

20 board feet.

A board 14 in. thick contains 14 times as many board feet as a board 1 in. thick, and a board 11⁄2 in. thick contains 1 times as many.

8. Find the number of board feet in a board 18 in.

wide, 16 ft. long, and 14 in. thick.

Since the board is 14 in. thick,

it contains 14 times as many board feet as a board 1 inch thick.

OPERATION

18 ÷ 12 = 1, width of board in ft. 1 × 16 × 1 = 30 board feet.

9. How many board feet are there in a board 2 ft. long, 6 in. wide, and 1 in. thick?

10. How many board feet are there in a board 2 ft. long, 1 ft. wide, and 2 in. thick?