with its arc as the length of the base, and the radius, the altitude. Since the sum of the arcs equals the circumfer

ence, the area of the circle is found by multiplying the circumference by the radius.

3035. Find the area of a circle whose radius is 60 inches.

SOLUTION

2 × 60 in. 120 in., the diameter; 3.1416 × 120 in. 376.992 in., the circumference; 30 × 376.992 = 1130.976 sq. in., the area.

NOTE. By cutting out a circle and a square of equal diameters from a board of uniform thickness, it is found that the weight of the circular board equals .7854 of that of the square board. But the circumscribed square equals 4 times the square of the radius. - Then the area of the circle equals .7854 times the square, or 3.1416 times the square of the radius.

3036. What is the area of a circle whose radius is 20.

3037. Find the area of a circle whose diameter is 36 inches.

3038. What is the area of a circle whose diameter is 20 inches?

3039. What is the area of a circle whose diameter is 40 inches?

3040. Find the area of a circle whose diameter is 36 inches.

3041. Find the area of a circle whose circumference is 160 feet.

3042. The circumference of a circular flower bed is 15.708 feet. What is its diameter? its area?

3043. Circumference, 314.16 feet. Find diameter and

area.

3044. Diameter, 100 feet. Find circumference and area. 3045. Radius, 60 rods. Find circumference and area. 3046. Area, 282.744 square feet. Find radius.

SUGGESTION. Area divided by 3.1416 equals R2.

R2=?

3047. What is the area of the largest circle that can be cut from a square board 22 inches long?

The Cylinder

3048. How many surfaces has a cylinder? What kinds of surfaces has it? What is the shape of the plane surfaces?

3049. Fold a sheet of paper in the form of a cylinder, holding the edges with your hands. Now pin or paste the edges together. What was the shape of your paper before you folded it?

3050. If you have a solid cylinder, how may the area of the curved surface be found?

3051. How is the entire surface of a cylinder found?

3052. Find the area of the curved surface of a cylinder whose circumference is 10 inches and whose height is 12 inches.

3053. The radii of the bases of a cylinder are each 7 feet and the height is 20 feet. What is the entire area ?

3054. How does a cylinder resemble a prism?

3055. What is the number of cubic inches in a prism whose base contains 300 square inches and whose height is 30 inches?

3056. What is the number of cubic inches in a cylinder whose base contains 300 square inches and whose height is 30 inches?

3057. What is the number of cubic inches in a cylinder a base of which contains 60 square inches, and whose length is 20 inches?

3058. A rectangular prism is 2 by 4 by 10 inches. Make a drawing of this figure and find the number of square inches in its surface.

3059. Diameter, 16 in., length, 16 in.; find surface and volume of cylinder.

3060. Diameter 3 in., length, 7 in.; find surface of cylinder.

3061. Radius, 10 in., length, 40 in.; find volume of cylinder.

3062. A standpipe is 14 feet in diameter and 125 feet high, inside measurement. How many cubic feet of water will it contain?

3063. What is the weight of this water if a cubic foot of water weighs 1000 ounces?

3064. A cylindrical piece of timber 60 inches long and 4 inches in diameter has how much surface?

3065. What is its volume?

SURFACES

3066. A has a farm of a mile wide and of a mile long. What are its dimensions in rods?

3067. How many acres of land are there in the farm?

1

3068. Draw a figure to represent this farm, allowing 16 of an inch to the rod. What are the dimensions of your figure?

3069. How many square inches are there in your figure? How many squares each of an inch long? Compare the number of these small squares with the number of square rods in the farm..

3070. A road 4 rods wide is made along the east and south sides of this farm. A strip of land 2 rods wide is taken from this farm for half of the road. What is this Show this on your

strip of land worth at $23 an acre? drawing.

3071. How many acres remain?

3072. How many rods of fence were required to inclose the land before the road was made? How many afterward?

3073. How many posts were required in each case if the posts were placed 1 rod apart?

3074. If the land is valued at $23 an acre and is assessed at 4 mills on the dollar on of its value, how much tax is produced?

3075. Before the road was made a partition fence divided the farm into two equal square fields. What are the di

mensions of those fields now?

3076. An orchard of 420 trees was planted in the form of a rectangle, with the trees one rod apart each way. How many acres does this orchard occupy?

3077. If each row contains 28 trees, how many rows are there? How many rows, if 21 trees were planted in a row? How many rows, if 35 trees were planted in a row?

3078. The house and garden occupy a rectangular plot of ground 12 by 16 rods, and the barn lot is 10 rods square. How many acres are there in each? in both?

3079. At the southwest corner of this farm there is a swamp. It may be cut off from the remaining portion of the farm by drawing an arc from the west side to the south side, with a radius 30 rods long, using the southwest corner as a center. How many acres does this swamp occupy? Express the decimal in square rods.

3080. Counting out the house lot, the barn lot, the swamp, and the road, how much remains for cultivation ?

3081. If the land under cultivation is planted in corn and produces 26 bushels to the acre, which is later sold at 41 a bushel, how much clear profit does the farm yield in one year, if the operating expenses amount to $268, and the farm is taxed at 11% on of its value?

3082. What per cent of profit does the owner realize on his investment?

3083. The second year the crop averages only 16 bushels to the acre and is sold for 30 a bushel. The operating expenses, taxes, etc., amount to $237.65. What per cent

of profit does he realize this year?

Review of Constructions

With compasses and ruler

3084. Construct a line perpendicular to another line at its middle point.