d. Square the root found and multiply it by 3 for a trial divisor and affix or add two ciphers. Find how often this is contained in the dividend and place the quotient in the result as the next figure of the root.

e. Multiply the last figure of the root by the rest and by 3 and add or affix one cipher, and write the result under the trial divisor.

f. Square the last figure of the root and place the result under the trial divisor.

g. Add together the trial divisor and the two quantities beneath it and this will be the complete divisor which multiply by the last figure of the root. Write the product under the dividend, subtract, bring down the next period, if any, and continue as before.

2. Find the cube root of 46656. 3. Find the cube root of 250047. 4. Find the cube root of 2000376. 5. Find the cube root of 5545233. 6. Find the cube root of 10077696. 7. Find the cube root of 46268279. 8. Find the cube root of 85766121. 9. Find the cube root of 153990656. 10. Find the cube root of 250047000. 11. What is the cube root of 926.859375?

12. What is the cube root of 44.6?

1. What is each side of a square box, the solid contents of which is 59319 cu. inches?

2. What is the length of each side of a cubic vessel whose solid contents is 2936.493568 feet?

3. A store has its length, breadth and height all equal; it can hold 185193 cubic feet of goods; what is each dimension?

4. How many linear inches must each dimension of a cubic vessel be which can hold 997002999 cubic inches of water?

5. What will be the length and depth of a bin which shall contain 160 bushels of corn, if its length is twice its width, and its depth and width are equal?

6. A bin is 18 ft. long, 12 ft. wide and 10 ft. deep. What must be the length of a cubical bin having the same volume?

7. Give the dimensions of a cube having the same volume as a box 5 ft. 4 in. long, 2 ft. 8 in. wide and 3 ft. 6 in. deep.

8. What is the surface of the six faces of a cube containing 91125 cubic feet?

9. A cistern in the form of a cube holds 150 barrels of water. What is each of its dimensions?

10. A cubical bin holds 350 bushels of wheat. What is its length?

11. Find the length of a cubical cistern which holds 5000 gallons of water.

MENSURATION

498. Mensuration is the art of computing lengths, surfaces and volumes.

499. A Line is that which has length only. All lines in mensuration and surveying are imaginary.

500. A Straight Line is the shortest distance between two points.

501. A Curved Line is a line having no part straight.

502. A Horizontal Line is a line parallel with the horizon, or with the water level.

503. A Vertical Line is a line perpendicular to the horizon.

504. An Angle is the space between two

lines which meet.

Thus the space between the lines A C and B C

is an angle, called the angle A C B.

505. A Right Angle is an angle formed by the meeting of a horizontal line and a perpendicular line.

An obtuse angle is one which is greater than a right angle. An acute angle is one which is less than a right angle.

506. A Surface is that which has length and breadth.

A Plane is a surface such that any two points of it can be joined by a straight line, which lies wholly in the surface. The application of a straight line is the test of a plane.

507. Area is a term applied to the quantity of surface contained in a figure having only length and breadth.

508. A Solid is that which has length, breadth and thickness. PLANE FIGURES

509. To find the area of a square or rectangle.

510. A Square is a figure having four equal sides.

511. A Rectangle is a figure having four right angles and its opposite sides equal.

The reason for the following rule will be found by referring to Art. 172.

A SQUARE.

A RECTANgle.

Rule. Multiply the length by the breadth, and the product will be the surface or area.

PROBLEMS

1. What will it cost to pave a sidewalk 80 ft. long and 15 ft. wide at $1.50 per sq. yard?

2. How much will a farm cost which is 185 rods long and 125 rods wide at $45 per acre?

3. How many small squares each containing 4 square inches, are contained in a large one which is 4 feet square?

4. What will it cost to plaster a room 15 ft. 6 in. long 12 ft. 9 in. wide and 10 ft. 3 in. high at 37 cents per square yard? yd. wide will cover a floor

5. How many yards of carpeting 16 ft. 9 in. long by 15 ft. 9 in. wide?

512. To find the area of a triangle.

513. The Base of a triangle is the side on which it rests. 514. The Altitude of a triangle is the perpendicular distance from the base to the opposite angle called the apex.

A D B

Since every angle in equivalent to one-half of a square or parallelogram having the same base, we may find the area of the squares or parallelogram and divide by two, or according to the following:

Rule. Multiply the base of the triangle by its height, and divide the result by two.

PROBLEMS

1. How many square yards in a triangle whose base is 27 yards and altitude 36 yards?

2. The gable end of a house was 34 ft. 6 in. from eave to eave and the perpendicular height of the ridge above the eaves is 13 ft. How many feet of boards will be required to cover three such gables?

3. A lot of ground 80 ft. long by 20 ft. wide was cut diagonally by a railroad, leaving a triangular plot of the same base and altitude; what was its area?

4. What is the rent of a triangular field whose base is 80 rods and perpendicular height 48 rods, at $4.50 per acre?

515. To find the circumference or diameter of a circle.

516. A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point within called the

center.

517. The Circumference of a circle is the curved line by which it is bounded.

518. The Diameter is a straight line drawn through the center, terminating at each end in the circumference.

519. The Radius is a straight line drawn from the center to the circumference, and is equal to half the diameter.

It has been proven in geometry that the circumference of every circle great or small is 3.1416 times its diameter, hence the

Rule. a. To find the circumference of a circle multiply the diameter by 3.1416.

b. To find the diameter of a circle divide the circumference by 3.1416.

PROBLEMS

1. What is the diameter of a circular piece of land measuring 5 miles around it?