13. Cut from thick cardboard or sheet metal a circle whose radius is 4 in. Cut from the same material a square whose side is 4 in. Weigh both, and see if the weight of the circle is not approximately 3.1416 times the weight of the square. Show that the result agrees with the rule that the area of a circle equals R2.

Problems involving Circles

1. The circular basin of a fountain is 20 feet in diameter. How many square feet in the bottom? What will it cost to cement the bottom at $1.75 per square yard?

2. Around the fountain basin is a

4-ft. paved walk.

How many square

feet of paving are needed?

SUGGESTION. -You are to find the difference between the area of a circle whose radius is 14 ft. and one whose radius is 10 ft.

3. The earth is nearly 8000 miles in diameter. What is the approximate length of the equator?

4. From the result of Exercise 3, find at what velocity a person who is at the equator revolves through space.

5. A boy gets 1 a square yard for cleaning the snow from a circular skating pond 300 ft. in diameter. How much does he earn?

6. What is the diameter of a circular sailor hat that requires 1 yd. 14 in. of velvet to bind it?

7. What part of a piece of buckram 10 in. square is left after cutting a circular piece 10 in. in diameter from it?

8. How many yards of lace will be required to trim 1 doz. plate doilies 6 in. in diameter, adding extra for fulling?

9. How many square feet of asbestos is used in making a table mat for a 54-in. circular table?

10. At 5 a foot, how much will it cost to put a fence around my circular tulip bed, if it is 8 ft. in diameter?

11. A hose will throw water 40 yd. in every direction from the hydrant. Over what area will it sprinkle?

12. Which is larger and how much, a circular tray 16 in. in diameter or a rectangular one 12 in. by 18 in. ?

13. If a circular piece of boiler plate 34 in. in diameter is cut from a sheet 3 ft. square, how many square inches of the metal are wasted?

14. A belt runs over a pulley 28 in. in diameter, revolving at a speed of 216 revolutions a minute. How far does a point on the belt travel in a minute?

15. If you can ride around 20 times on a merry-go-round for 5, and your path is 20 ft. in diameter, how far do you ride for 5?

22. RECTANGULAR PRISMS AND THEIR VOLUMES

1. Describe a right prism.

2. Prisms are named from their bases: square, rectangular, triangular, hexagonal, etc. Name some objects that are square prisms; some that are rectangular.

3. Is a square prism also rectangular? What kind of prism is a cube ?

4. To find the volume of a rectangular prism whose dimen sions are 4 in., 5 in., and 9 in.

(1) First find the number of cubic inches in one row or a square prism 1 in. by 1 in. by

9 in.

(2) Then find the number of such rows in one tier or layer 4 in. wide.

(3) Then find the number of such layers in the prism, and explain the statement 5 x 4 x 9 cu. in. =

cu. in.

9

5

5. How many inch cubes may be put into a box 10 in. long, 8 in. wide, and 5 in. deep?

6. A trunk measures 3 ft. by 20 in. by 18 in. Find its volume.

Find the volumes of rectangular prisms of these dimensions:

13. If the base of a rectangular prism contains 30 sq. in., how many cubic inches in the bottom layer? If the prism is 10 in. high, how many cubic inches in the prism?

STATEMENT.-10 x 30 cubic inches

=

cubic inches.

14. The floor of a cellar contains 36 sq. yd. If the cellar is 8 ft. deep, find its cubical contents.

15. A square prism is 16 in. wide and 4 ft. long. Find the volume.

16. A 5-in. cube is cut from the corner of a 20-in. cube. What part remains?

17. A cellar is 40 ft. long, 30 ft. wide, and 7 ft. deep. How many cubic feet of earth were removed in its construction? How many loads (cubic yards)?

18. A freight car 36 ft. long and 81 ft. wide is loaded 5 ft. deep with wheat. How many bushels does it contain if 1 cu. ft. = 0.8 bu.?

19. How many tons of ice can be packed in an ice house 40' x 24' x 16', allowing 2' on each side and above and below for sawdust? (1 cu. ft. of ice weighs 56 lb.)

20. An ice pond is 260 ft. wide and 426 ft. long. If the ice is frozen to a depth of 14 in, how many tons can be cut from the pond?

21. My ice box will hold a piece of ice 32′′ × 24′′ × 14′′. How much will such a piece weigh?

22. A coal bin 12 ft. long and 8 ft. wide is filled to the depth of 5 ft. Allowing 80 lb. to a cubic foot, how many tons are in the bin?

23. A coal car 7 ft. wide and 30 ft. long is loaded to an average depth of 4 ft. How many tons of coal on the

car?

23. THE SURFACES OF RECTANGULAR PRISMS

1. How many surfaces has a rectangular prism?

2. What name is given to a rectangular prism with equal faces?

3. Find the entire surface of a 5-in. cube.

Explain the statement: 6 x 5 x 5 sq. in. =

==

sq. in.

4. The entire surface of a cube is 150 sq. in. How long

How long a cube has

8. An entire surface of 384 sq. in.? 9. An entire surface of 600 sq. ft.?

10. An entire surface of 294 sq. in.?

11. Compare the ends of a square prism with each other. 12. Compare its four sides.

13. Find the entire surface of a square prism 8 in. long and 3 in. wide. (What is the area of each square? How many? Of each rectangle? How many?)

14. Compare the opposite faces of any rectangular prism.

15. Give the dimensions in feet of each face in the figure at the right. What is its entire surface in square feet?

Find the entire surfaces of prisms:

16. 10 in. by 6 in. by 4 in.

6'

2'

19. How many square yards of lath does it take for the walls and ceiling of a room 14 ft. wide, 18 ft. long, and 9 ft. high?

20. How many square feet of sheathing does it take for the two sides and two ends of a box car 8 ft. wide, 8 ft. high, and 34 ft. long?