55+ AREA OF CIRCLE Draw a large circle and divide it into a large num FIGURE 1 ber of equal sectors. Cut into semicircles. Cut each semicircle along the line dividing it into sectors. Arrange the parts of one semicircle as in the lower part of figure 2. Arrange the parts of the other semicircle as in the upper part of figure 2. The figure produced is practically a parallelogram whose base is of the circumference of the circle and whose altitude is the radius of the circle. The area of a circle is equal to one half the product of ite circumference and its radius. Calling the circumference 3 times the diameter, find the area of: 1. A plate 7 inches in diameter. 2. A circular table 28 inches across. 227 AREA OF CIRCLE 233 3. A piano stool 14 inches in diameter. A circular bed of pansies, if the bed is 35 inches in diameter. 5. A circle drawn with a 3-foot radius. A button 12 inches in diameter. 7. A medal whose circumference is 22 inches. 8. A circular window the distance around whose edge is 5 feet 6 inches. та 140 A watch crystal 1 inches in diameter. 10. A 50-cent piece, diameter 12 inches. Find the exact area of: The base of a tin pail whose diameter is 8 inches. 2. The end of a log 15 inches in diameter. 3. The surface covered by the bottom of a pitcher 5 inches across. A clock dial whose radius is 4 inches. 5. The largest circle that can be drawn on a piece of paper 7.5 inches square. May 15 1. Find the area over which a cow can feed if tied to a stake by a rope 28 feet long. (Use 34.) 2. The curbing about a circular pond is 78.54 feet. Find the area covered by the pond. (Use 3.1416.) 3. The bottom of a barrel is 1 foot 9 inches in diameter. What area does it cover on the floor? (Use 31.) 4. What is the area covered by the base of a circular kettle 15 inches in diameter? (Use 3.1416.) 5. At 12 cents a foot, how much will it cost to fence a circular bed of tulips if the distance across the bed is 56 inches? (Use 34.) 6.A farmer has a well 31 feet in diameter. the area of the opening? (Use 34.) What is 7. Find the approximate area of the base of a circular chimney 35 feet in diameter; the exact area. CYLINDER: SURFACE, VOLUME Of what shape are the ends or bases of this solid? How do they compare in size? If the bases are equal and parallel, what is true of their diameters? What is true of the diameter of the whole solid? 4 6 A solid of uniform diameter whose bases are equal and parallel circles is a cylinder. The altitude of a cylinder is the perpendic ular distance between its bases. The lateral or curved surface of a cylinder is the conver surface. 10 Exactly fit a piece of paper around a cylinder. What form has it when unrolled? How does the length of the rectangle compare with the circumference of the base? How does the width of the rectangle compare with the altitude of the cylinder? How can the convex surface of a cylinder be found? 27 CYLINDER: SURFACE, VOLUME 235 The convex surface of a cylinder is equal to the product of its circumference and its altitude. The entire surface of a cylinder is equal to the sum of the convex surface and the areas of the bases. 1. What is the convex surface of a cylinder whose cir cumference is 14 in. and whose altitude is 3 ft.? Find the convex surface of these cylinders: 25 8. Find the entire surface of the above cylinders. 9. What is the convex surface of a stovepipe 7 in. in 10. A tin dish is 5 in. in diameter and 10 in. high. 11. What is the entire outside surface of a log 25 in. in 12 At 12 a square yard, how much will it cost to paint If the base of this cylinder covers 2 sq. in., Tell how to find the volume of a cylinder. The volume of a cylinder is found by multiplying the area of its base by its altitude. Mr. Merriam has a silo 17.5 ft. in diameter and 25 ft. high. What is its capacity in cubic feet? 8. How many gallons of water will be required to fill a kettle whose diameter is 14 in. and whose height is 12 in.? 33 9. A water tank by the side of a railroad track is 12 ft. in diameter and 15 ft. high. Find its capacity in gallons. 10. A copper hot water boiler is 15 in. in diameter and 4 ft. high. How many square feet of copper were required to make it? What is the capacity of the boiler in gallons? า 11 An iron ash can whose base covers 31 sq. ft. is 2 ft. 4 in. deep. Find its capacity. PERCENTAGE The expression per cent means by hundredths. Oral Thus, 3 per cent of a dollar means 3 hundredths, or 03, of a dollar. The sign % means the same as the expression per cent. Thus, 7% of a dollar and 7 per cent of a dollar mean the same thing-7 hundredths, or .07, of a dollar. 1. Into how many hundredths can a dollar be separated? A ton of coal? A yard of cloth? Anything? |