Written.

REVIEW

89

1. Find the exact interest on $6,000 from July 5 to Sept. 16 at 6%.

2. Find the discount and proceeds of the following note: Face, $550; date of note, May 3, 1905; time to run, 6 mo.; date of discount, May 3, 1905; rate of discount, 5%.

3. Find the discount and proceeds of the following note: Face, $3,500; time, 90 da.; discounted on the day of date at 6%.

4. Mr. Black sold a suburban farm of 12 acres. The land was sold at $800 per acre, and the buildings at $2,500. The purchaser paid $3,000 cash and gave a note for the balance at 51% per annum. What was his annual interest payment?

5. Mr. Black lent the $3,000 received at 43% per annum. What was Mr. Black's total annual income, according to Exercise 4, from the sale of his farm?

6. A merchant bought 4 boxes of tea containing 125 lb. each. The price was 76¢ per lb. cash, but the seller agreed to wait 3 mo., charging 6% interest. What was due at the

end of 3 months?

7. A man bought a lot for $480. He paid $10 down and agreed to pay $10 each month thereafter, together with interest at the rate of 6% per annum on the unpaid balance. What was his first monthly payment? His second payment? His fourth?

8. A demand certificate of deposit for $800 dated May 3, interest at 2%, was presented for payment Sept. 29. How much interest was received?

9. Mr. George deposited $50 in the savings bank Feb. 1; $75 Mar. 1; $100 Apr. 1 and $50 May 1. How much interest, allowed from date of deposit, was credited to him July 1?

10. A 90-day note dated Jan. 5, face $6,000, was discounted Mar. 1 at 6%. Find the proceeds.

FORM STUDY AND MEASUREMENT

Written.

CIRCLES

1. Review the definitions and results of page 26. What is the cost of a floor for a round tower 40 ft. in diameter at 324 per square foot?

2. A round tree trunk has a circumference of 14.13 ft.; what is its diameter? What is the area of a cross section? Use π3.14.

3. A target is 8 ft. in diameter, the bull'seye is 2 ft. in diameter, and each of the rings formed by the other circles is 1 ft. wide; what part of the whole target is the bull'seye? Each ring?

4. The rotunda of the capital in Washington is a circular hall 98 ft. in diameter; find the cost of a stone floor for it Use π = 22.

at 49¢ per square foot.

5. A semicircular platform 20 ft. in diameter is to be carpeted with carpet 1 yd. wide, costing $1.20 a yard. Allowing 5% of the area of the platform for waste in fitting, what is the cost?

6. Find the cost of clearing a circular skating space 500 ft. in diameter, if the snow is 7 in. deep on the ice and the cost of removal is 15¢ a cubic yard.

7. A cow is tethered in the center of a field 100 ft. square with a rope 50 ft. long; over how many sq. ft. can she graze? Over what fractional part of the field?

8. The earth is about 8,000 mi. in diameter and makes one rotation on its axis in 24 hours; how far does a point on the equator move in a day? An hour? A minute?

Written.

MEASUREMENT-CYLINDERS

91

1. Review the definitions and results of pp. 28-29. How many square feet of sheet-iron will it take to make 10 lengths of stovepipe 6 inches in diameter, each length being 18 in. long? (Use π = 22.)

2. What will it cost to paint the surface of a standpipe 52 ft. in circumference and 68 ft. high, with open top, at 35¢ per square yard?

3. How many cubic yards of water will the pipe hold?

4. The pit for a turntable is 24 ft. in diameter and 4 ft. deep. Find the cost of excavation at 70¢ per cubic yard.

5. A sprinkling wagon has a cylindrical tank 12 ft. long and 4 ft. in diameter; how many gallons does it contain? (Use 71 gal. = 1 cu. ft.)

6. What will it cost to paint the sides and top of a gas tank 300 ft. in circumference and 60 ft. high at 334 per square yard?

7. How many cubic feet of gas will the tank contain?

8. A drain pipe has an internal diameter of 30 in. It is half full of water which flows at the rate of 2 miles per hour; how many cubic feet of water pass any point per minute?

9. A pillar 21 ft. high and 3 ft. in diameter is to be covered on the Fourth of July; equal quantities of red, white, and blue bunting are used. How many yards of each must be bought?

10. At 7 A.M. a gas tank 220 ft. in circumference is 10 ft. high. At 5 P.M. it has been raised to the height of 40 ft. by the manufactured gas, none having been consumed; how many cubic feet of gas have been manufactured per hour?

II. The production continuing at the same rate, the height of the tank had diminished to 4 ft. by 1 A.M. Find in cubic feet the average hourly consumption from 5 P. M. to 1 A.M.

92

MEASUREMENT-SURFACES OF CONES

Instruments: Rule, compasses, and scissors

1. Draw a circle of 3 in. radius. Cut along the circle and along a diameter.

2. Roll one of the pieces of paper into a form like the icecream mold and place it upright on a sheet of paper.

Such a figure is called a cone.

3. Mark around the base of the cone. What is the figure thus made?

4. Measure the diameter of this circle. circumference.

Compute its

5. Compare the result with the length of the original circle. Why should this be so?

6. Draw on paper a semicircle of 4-inch radius. Fold through the middle so as to make a line like OC in the figure. Fold OA and OC so as to make the line O D. Cut along this line.

7. What part of the area of the circle is that of the sector, OD CB? What is the area of the sector?

A

D

B

8. Roll the sector into a cone; what is the area of the surface of this cone?

9. From a circle of 2-inch radius cut a sector whose area is that of the circle; how many sq. in. in the area of the sector? What would be the area of the cone thus made?

10. What is the area of the surface of a cone made from a sector that is of a circle of radius 6 in. ?

II. Lulu rolled a cone on a paper, keeping its vertex stationary, and marked the path traced by the base until the cone made one turn. She connected the ends of the arc traced with the position of the vertex. What kind of a figure was formed?

MEASUREMENT-SURFACES OF CONES

93

1. Cut from cardboard a right-angled triangle having one perpendicular side longer than the

other.

2. Set the triangle upright on a piece of paper, as shown in the picture, and rotate it about the vertical line O B.

3. What figure does the point A trace on the paper?

4. As the triangle rotates about B O, what kind of a figure does the hypotenuse generate?

Slant Height, Vertex, and Altitude of a Cone. The length of the hypotenuse is called the slant height of the cone. The top point of the cone is called its vertex. The perpendicular distance from the vertex to the base is called the altitude.

5. When a sector of a circle is made into a cone what does the arc of the sector become? What does the radius of the sector become? How is the area of a sector found?

The lateral area of a cone is the product of the perimeter of its base and the length of the slant height.

6. How many square inches

of material are

there in the crown of this hat, if the band is 18 in. long?

7. Roy and Harold made a tent for camping. The radius of the base was 6 ft. and the slant height 16 ft. How many square feet were there in its surface?

8. How many sq. yd. of duck were needed to make this tent? What did it cost at 1214 a yd., allowing

for waste?