VOLUME OF A CYLINDER

346. The figure represents a cylinder whose base has an area of 4 square inches. How many cubic inches in one layer 1 inch high?

If the cylinder is 4 inches high, how many cubic inches does it contain?

4 cu. in. in 1 layer.

4 (layers)

16 cu. in. in the cylinder.

Volume of a cylinder = area of the base × height (h) = πr2 × h.

Find the volume of a cylinder 2 in. in diameter and 4 in. high.

Tr2 (the area of the base) = 3.1416 sq. in.

4 in. (height) × 3.1416 = 12.5664 cu. in., solid contents, or volume.

Find the volume of a cylinder having a diameter of 8 in. and altitude of 12 in.

SUGGESTION: πr2 = 3.1416 x 16 = 50.2656 sq. in. in base. πr2 × h = ?

1. A cylinder is 4 in. in diameter and 12 in. high. What is its volume?

2. If its diameter and its height were both doubled, what would the volume be?

3. Which of the following are cylinders: a cheese, stove pipe, a silver dollar, a lead pencil, a piece of pipe?

4. Take the necessary measurements of some cylinder in your schoolroom.

its volume.

Draw a diagram of it to scale, and find

347. Solve:

WRITTEN EXERCISES

1. Find the number of cubic feet of earth that will be removed in digging a cistern 4 feet in diameter and 18 feet deep.

2. A circular pond was 2,500 feet in diameter, and had an average depth of 5.5 feet. How many cubic feet of water did it contain?

3. How many cubic yards of earth will be removed in digging a circular pit 12 feet in diameter and 3 feet deep?

4. In a church there were 12 stone pil

lars, each 18 feet high and 7.854 feet in circumference. How many cubic feet of stone in all the pillars?

5. How many cubic feet of water in a cylindrical boiler 4 feet in diameter and 61 feet long?

6. Mr. Westcott dug a well 24 ft. deep and 6 ft. in diameter. How many cubic feet were excavated?

7. He lined it with a stone wall 1 ft. thick. What was the diameter of the well

then?

8. When water stands in it 8 ft. from the top, how many gallons does it contain?

9. A square curb is built over the well, 4 ft. high and just reaching to the outside of the stone lining. How many feet of boards are required for the curb?

10. Mr. Horton built a silo* near his barn. It was 10 ft. in diameter and 20 ft. high. How many square feet of lumber were required to cover the sides?

*NOTE. A silo is a cylindrical building used to hold certain kinds of feed for cattle, called ensilage.

will a pipe 6 in. in diameter and 1 mile long hold?

15. The new gas house is 25 ft. in diameter and 40 ft. high when fully distended. How many cubic feet of gas will it contain?

16. Mary's mother made a cake for her on her tenth birthday. Its diameter was 10 inches and its height 3 inches. What was its circumference? How many square inches in its top? How many cubic inches of cake were there in all?

17. If the cake was cut into eight equal pieces, what was the length of the arc of a circle represented by the rounded part of each piece?

18. How many degrees in the acute angle of each piece?

CAPACITY IN GALLONS *

348. How many cubic inches are there in a gallon?
How
many cubic inches are there in a cubic foot?

* Represent 1 gallon and 1 cubic foot, either by having the actual measures, or something about the same size, as a waste basket, hat box, can, etc.

7111 times

=

231)1728 cu. in.

= 111, nearly 1. There are ap.

proximately 7 gallons in 1 cubic foot. In problems use 7.

1. How many gallons in 2 cubic feet? 2. How many gallons in 10 cubic feet?

3. How many gallons in 20 cubic feet?

How many gallons of water will a tank hold that is 5 feet in diameter and 6 feet deep?

3.1416 x 6.25 = 19.635000 sq. ft., area of base.

19.635 sq. ft in base.

6 (altitude)

117.810 cu. ft. in tank.

7.5 x 117.81 883.575 gallons of water in the tank.

349. Solve:

=

WRITTEN EXERCISES

1. How many gallons of water can be let into a cylindrical swimming tank 40 feet in diameter and 8 feet deep? Into a tank 361 feet in diameter and 9 feet deep?

2. How many gallons of water will be contained by a round boiler that is 3 feet in diameter and 8 feet high? By one that is 5.5 feet in diameter and 12.4 feet high?

3. How many gallons of oil will the cylindrical tank on an oil wagon hold, if it is 43.9824 feet in circumference and 15 feet long?

4. How many hours will it take to empty a cylindrical tank whose diameter is 10 feet and altitude 12 feet, if the pipe that carries off the water empties 12 gallons per minute?

!

5. How many gallons of water will a cylindrical cistern contain, whose diameter is 3 feet and depth 15 feet?

6. How many gallons of paint will a cylindrical vat contain that is 6 feet in diameter and 4 feet deep?

7. The Central Railroad of New Jersey erected a cylindrical water tank to supply their trains. This tank was 12 feet in diameter and 20 feet high. How many gallons of water would it hold?

8. How many gallons of water can be held at one time in a hose whose diameter is 2 inches and length 500 feet? (Use 231 inches to a gallon.)

9. In a factory there are six boilers, each 5 feet in diameter and 9 feet long. How many gallons of water will all six contain?

10. There are 31

will 63 gallons fill?

gallons in a barrel. How many barrels 126 gallons? 315 gallons?

11. How many barrels can be filled with oil from a tank 14 feet in diameter and 7 feet deep?

12. The Northern Pacific Railroad erected a water tower for supplying passing trains. This tower was 47.124 feet in circumference and 22 feet high. How many square feet of sheet iron were required to line it?

13. How many gallons of water will this tower hold?

14. How many cubic feet of ice can be cut from a circular pond 120 feet in diameter, if the ice is frozen to the depth of 21 feet?

15. A New Orleans mill had a vat 12 feet in diameter and 4 feet deep. How many barrels of molasses could be filled from the contents of this tank?

16. How many cubic feet of earth will be removed in digging a well 3 feet in diameter and 10 feet deep?