MEASUREMENT OF CYLINDERS

1. These boys measure the circumference and the height of this water tank and find them to be 33 ft. and 18 ft. respectively. Find the diameter, the area of the base, and the volume.

Find the volumes of cylinders whose heights and areas of base are respectively as follows:

2. 13 in., 27 sq. in. 3. 15 in., 88 sq. in. 4. 43 in., 481 sq. in.

Find the heights of cylinders whose volumes and areas of base are respectively as follows:

5. 22.5 cu. ft., 7.5 sq. ft.

6. 197.6 cu. ft., 30.4 sq. ft.

Formerly the volume in Ex. 5 would be given as 22 cu. ft. 864 cu. in.

Find the areas of base of cylinders whose volumes and heights are respectively as follows:

7. 324 cu. ft., 18 ft.

8. 33.15 cu. ft., 2 ft. 2 in.

Find the volumes of cylinders whose heights and radii of base are respectively as follows:

9. 27 in., 4 in.

10. 32 in., 8 in.

11. 2 ft. 6 in., 2 in.

Curve Surface of a Cylinder. If we slit the curve surface of a cylinder and spread it out flat, what will it become? How may we find the area of this surface? Try it with a paper cylinder. What is the area of the curve surface of a cylinder of height 6 in. and circumference 8 in. ?

It is the same as that of a rectangle 6 in. by 8 in., or 48 sq. in. We see that the area of the curve surface of a cylinder is equal to the circumference multiplied by the height.

or

That is,

area = circumference x height,

area = 22 × diameter x height.

SURFACE OF A CYLINDER

Numbers 1 to 12, oral

State the areas of the curve surfaces of cylinders with heights and circumferences as follows:

13. How many square inches are there in the curve surface of a wire of circumference 1 in. and length 200 ft.?

14. How much sheet iron will be needed for a pipe 8 ft. long and 6 in. in circumference, allowing 1 sq. ft. for overlapping? 15. A tin cup is 7 in. in circumference and 3 in. high. How many square inches of tin are needed for the curve surface? In Exs. 15 and 16 the measurements include the overlapping.

16. How many square feet of galvanized iron are needed for a water pipe 10 ft. long and 9 in. in circumference?

USING WHAT YOU HAVE LEARNED

1. Write a rule for finding the circumference of a circle, given the radius; also for finding the area of the circle.

2. How many square inches of surface are there on a wire 59 ft. long and in. in circumference?

3. If the height and diameter of a solid cylinder are each 8 in., what is the total area of surface?

The teacher should explain that to the cylindric surface should be added the areas of the circles forming the bases.

4. How many square inches of tin are needed for a cylindric cup 4 in. high and 4 in. in diameter?

5. How many square feet are there in the curve surface of a water tank that is 40 ft. high and 127.3 ft. in circumference?

6. How many square feet of surface are there on the outside of a smokestack 30 ft. high and 2 ft. in exterior diameter ?

7. The curve surface of a granite cylindric shaft 3 ft. 6 in. in diameter and 22 ft. 3 in. long is to be polished. How many square feet of surface are to be polished?

8. In a certain factory there is a room heated by 210 ft. of steam pipe of diameter 2 in. Find the radiating surface; that is, find the area of the curve surface which radiates the heat.

9. A large suspension bridge has 4 cables, each 1872 ft. long and 1 ft. 2 in. in diameter. In letting the contract for painting these cables it is necessary to know their surface. Compute the area to be covered.

10. In making metal bedsteads some iron rods 0.7 in. in diameter are covered with thin rolled brass. Suppose that a shop needs 6000 ft. of such rods, how many square feet of rolled brass will be needed, not allowing for waste?

1. Henry helps his father at the market. They have been buying grapefruits, 64 to a box, at $5.50 a box, and selling the grapefruits at 12¢ each, averaging two boxes a day. Another dealer sells two boxes a day of larger grapefruits, costing $6.50 per box of 48, at 20¢ each. Henry thinks it would be better to deal in the larger fruit. Is he right? What is the difference in net income on the grapefruits per day?

2. They buy lemons at $8.10 for a box of 360, selling them at 35¢ a dozen. How much do they gain on a box? What per cent do they gain on the cost? on the selling price?

3. Henry's father pays $28 a month for the rent of his stall in the market, $6.25 a month for light, and $9.25 a day for help, besides allowing Henry 15¢ an hour. Henry works 12 hr. a week. There being 306 market days in a year, how much are the expenses for a year?

INDUSTRY IN THE SCHOOL

1. The class made this bookrack. If the rack will hold 12 books 1 in. thick, how many books in. thick will it hold?

2. The inside length of the shelf is 18 in., each end piece is 14 in. thick, and the shelf projects 14 in. at each end. What is the total length?

3. The end pieces are 6 in. high. The shelf is 41 in. wide, and the

greatest width of the end pieces is 57 in. Taking the total length of the shelf as found in Ex. 2, what length of board 6 in. wide will be needed for the entire rack, allowing in. for waste in sawing and dressing?

4. The price of 1-inch lumber of this kind is $160 per M. This means, as we have already learned, that 1000 sq. ft. of boards 1 in. thick cost $160. At this rate, how much will 1000 sq. ft. of boards 14 in. thick cost?

5. If a shelf requires a board 32 in. long and 6 in. wide, how many square feet will such a board cover?

6. If two boards, each 16 ft. long and 6 in. wide, are required to make a set of shelves, what is the cost of the lumber at $140 per M if the boards are 1 in. thick? if they are 14 in. thick?

7. If a shelf is 41 in. wide and 18 in. long, the width is what fractional part of the length? what per cent of the length?

8. If an end piece is 6 in. high and 57 in. wide, the width is what fractional part of the height? what per cent of the height?

9. If an end piece is 14 in. thick and 61⁄2 in. high, the thickness is what fractional part of the height? The height is what fractional part of the thickness? what per cent of the thickness?