CHAPTER LX.

1. If 6 pounds of sugar cost $0.30 what will 10 pounds cost?

2. If a man earns $60 in 3 weeks how much will he earn in 7 weeks?

3. If 10 tons of coal cost $60 what will 12 tons cost?

4. If 7 cords of wood cost $35 how many cords may be bought with $85?

5. What will 7 barrels of flour cost if 3 barrels cost $18?

6. If 0.75 of a ship cost $6000, what will 0.625 of it cost?

7. If the interest of $100 for a given time is $12, what principal will gain $30 in the same time ?

8. If a steeple 160 feet high casts a shadow 240 feet, what is the length of a shadow cast, at the same time, by a staff 6 feet high?

9. If a staff 6 feet high cast a shadow 7 feet, what is the height of a steeple which, at the same time, casts a shadow of 150 feet?

10. If a man's salary amounts to $6000 in 5 years, what will it amount to in 9 years?

CHAPTER LXI.

1. What is the second power, or square, of 2?

The second power, or square, of a number is that number taken twice as a factor.

2. What is the third power, or cube, of 5? 3. What is the fourth power of 4 ?

4. Compare the square of 6 with the cube of 3. 5. From the square of 10 take the fourth power of 3.

6. To the cube of 4 add the square of 6.

7. What is the cube of ??

8. Take the square of from the square of . 9. What is the square of 21?

10. What is the square of 0.25?

11. From the square of 0.8 take 0.44, and find the cube of the remainder.

12. The square of 9 is how many times the cube of 3?

13. Divide the square of 10 by the square of 5. 14. What is the difference between the cube of 4 and the cube of 5?

the

15. From the fourth power of 5 take 3 times square of 10.

CHAPTER LXII.

1. Find two equal factors whose product is 25. 2. Find three equal factors whose product is 27.

A root of a number is one of the equal factors whose continued product is that number. The square root of a number is one of two equal factors. whose product is that number. The cube root is one of three equal factors whose product is that number.

3. What is the square root of 16? 4. What is the cube root of 125 ? 5. What is the square root of 18?

6. What is the cube root of?

27

7. Add the square of 6 to the cube of 4 and find the square root of their sum.

8. What is the square root of 0.64 ? 9. What is the square root of 24 ?

10. What is the cube root of ?

11. What is the cube root of? Of 3} ?

12. Add the square of 4 to the square of 3, find the square root of their sum, cube this result, subtract 25, find the square root, cube this result, divide by 4, and find the square root of of the result obtained.

CHAPTER LXIII.

1. In the figure, ABCD, at the right, into how many parts is AD divided? Into how many is AB divided?

B

A

In the figure ABCD, of four sides, if the angles are equal each angle is called a right angle, and the figure is called a rectangle. If the sides of a rectangle are equal to one another, the figure is a square. AD is the base and AB the altitude of the rectangle.

2. In the rectangle ABCD, how many small squares are there in the lowest row of squares? How many such rows are there in the whole figure? How many small squares in the whole rectangle ABCD?

The number of square units in a rectangle is called the area of the rectangle, and is equal to the number of linear units in the base multiplied by the number in the altitude.

Stated in its usual form,

The area of a rectangle is equal to the product of its base by its altitude.

3. What is the area of a rectangle whose base is 15 feet and altitude 12 feet?

4. What is the area of a rectangular field 20 rods long and 8 rods wide?

5. If the area of a rectangle is 55 square inches and the base is 11 inches, what is the altitude?

In the figure at the right the lines AD and BC, having the same direction, are said to be parallel; so AE is parallel to DF; and AB to DC.

E B

A

F C

D

The figure ABCD whose opposite sides are parallel is called a parallelogram. FD or EA is the altitude of the parallelogram.

6. How does the figure AEB compare with DFC? How does the parallelogram ABCD compare with the rectangle AEFD? How then can we find the area of a parallelogram?

7. What is the area of a parallelogram whose base is 13 feet and altitude 5 feet?

The figure ABC at the right is called a triangle. AC is the base and BD the altitude of the triangle.

B

A D

E