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4. How many 3 inch cubes may be cut from a 12 inch cube? ANS. 64. 5. How much will it cost to dig a cellar 8 feet square and 8 feet deep, at 25 cents per cubic yard?

ANS. $14.223.

6. How many gallons of water will fill a cistern 10 square and 10 feet deep?

feet

ANS. 7480 gallons, wine measure. 6127189 gallons, bear measure. 7. How many cubic feet are there in a box which measures 3 feet 6 inches on each side?

The inches may be changed to decimals or duodecimals. ANS. 166 cubic inches. 8. How many 4-inch cubes and 8 inch cubes, of each an equal number, may be cut from one 12 inch cube? ANS. 3 four-inch cubes, and 3 eight-inch cubes.

SECTION III.

A Parallelopiped.

Parallelopiped is a solid having six sides, the opposite

sides being equal and parallel planes.

To find the solidity of a parallelopiped.

Multiply the area of one end by the length, and the product will be the solidity.

1. What is the solidity of parallelopiped, the base of which 16 inches square and length 50 inches?

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16x16 256 sq. inches, area of one end A B C D. 256×50=12800 cubic inches, solidity of the paral

lelopiped.

2. How many cubic feet are there in a timber 20 feet long, the ends of which are 2 feet square?

ANS. 80 cubic feet.

3. In a stick of timber 18 inches square and 15 feet long, how many cubic feet?

ANS. 33 cub. feet.

If two of the dimensions are given in inches and one in feet, multiply the dimensions together and divide the product by 144; the quotient will be cubic feet.

4. What is the solid measure of a mahogany plank 15 feet long, 2 feet wide, and 5 inches thick?

ANS. 12 cubic feet.

If one of the dimensions be given in inches and the other two in feet, multiply the dimensions together and divide by 12; the quotient will be cubic feet.

15X2=30 sq. feet, this gives the area of the surface. 30X5=150, this gives twelfths of cubic feet. 150-12-12 cubic feet.

5. How far from the end must a timber be cut which is 12 inches wide and 8 inches thick, so that the piece may contain 1 cubic foot? ANS. 18 in.

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6. How many cubic inches may be placed in a box which measures inside, 4 feet in length, 24 feet in width, and 3 feet in depth?

4X2 X3-30 cubic feet.

1728X30 51840 cub. in.

1 cubic foot is 1728 cubic inches.

7. How many gallons of water will fill a vessel 4 feet long, 3 feet wide, and 5 feet deep?

Change the cubic feet to cubic inches, and divide by the number of cubic inches in a gallon.

ANS. 448.8 gallons, wine measure.

8. How many cubic feet of earth must be removed, to form a cistern 8 feet square and 10 feet deep? How many gallons of water will the cistern contain ? ANS. 4787.4 wine gallons. 9. How many cubic feet in a stick of timber 25 feet long, 21 inches wide, and 18 inches thick?

ANS. 65 cubic feet.

SECTION IV.

Wood Measure.

A pile of wood 4 feet long, 4 feet wide, and 4 feet high, is half a cord. Two such piles is a cord.

1. How many cubic feet in a cord of wood?

ANS. 128 cubic feet.

2. How many cords in a pile of wood 12 feet long, 4 feet wide, and 8 feet high? ANS. 3 cords.

3. How many cords in a pile of wood 127 feet long, 16 feet wide, and 20 feet high? ANS. 317 cords. 4. A pile of wood 4 feet long, 4 feet high, and 1 foot wide, is a foot of wood. How many cubic feet in a foot of wood? ANS. 16 cubic feet.

5. How many feet of wood are there in a cord?

ANS. 8 feet.

6. How many feet of wood are there in a load 8 feet long, 4 feet wide, and 6 feet high?

ANS. 13 feet.

Wood for fuel is usually cut 4 feet in length, and placed in carts and wagons in two ranges, one behind the other; the load then is 8 feet long; therefore, in measuring the number of feet of wood, it is unnecessary to multiply by the length when it is exactly 8 feet, for multiplying half of the height by the width gives the number of feet of wood.

From this may be deduced the following rule for measuring loads of wood and bark.

If the load be 8 feet long, multiply the width by half the height; the product is the number of feet of wood.

7. How many feet of wood in a load 8 feet long, 5 feet wide, 6 feet high? ANS. 15 feet.

8

Half of 6 is 3, and 5X3=15. In a load of wood 8 feet in length, 4 feet in width, and 4 feet in height, how many feet?

ANS. 9 feet.

Half the width is 2, 44X2-9. 9. If a load of wood measures 8 feet long, 51 feet wide, and 7 feet high, how many feet of wood does it measure? ANS. 191 feet. 10. How much will be the cost of a load of pine wood which is 8 feet long, 4 feet wide, and 9 feet high, at 60 cents per foot? ANS. $12,15.

11. What will be the cost of a load of oak wood which is 8 feet long, 4 feet wide, and 6 feet high, at 80 cts. per foot? ANS. $10,80. 12. If wood be $6 per cord, how much is it per foot? ANS. 75 cents.

How much will a cord of wood cost at five shil

13.

lings and three pence per foot?

ANS. $7,00.

SECTION V.

A Prism.

A Prism is a solid, the ends or bases of which are equal and parallel plane triangles or polygons, and the sides plane parallelograms.

To find the solidity of a Prism.

Multiply the area of its base by the length.

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