SUMMARY OF CHAPTER X

56. To find the area of a square or rectangle, multiply the length by the width. (Sec. 101.)

57. To find the length of the circumference of a circle when the diameter is given, multiply the diameter by 3.1416. (Sec. 102.)

58. To find the diameter of a circle when the circumference is given, divide the circumference by 3.1416. (Sec. 102.)

59. To find the volume of a cube or rectangular block, multiply the length by the width and this again by the thickness. (Sec. 103.)

60. To find the weight of lumber, multiply the number of cubic feet in the closely stacked pile by the weight per cubic foot. (Sec. 104.)

61. To find the weight of any quantity of building material, multiply the quantity in cubic feet by the weight per cubic foot.

(Sec. 105.) 62. To determine the size of footings, divide the weight of the wall in tons per lineal foot by the bearing power of the soil in tons per square foot. The result will be the required area of the footing in square feet per lineal foot of wall. (Sec. 106.)

63. To find the quantities of materials for concrete work, multiply the number of cubic yards of concrete by the value for the required mixture given in the table. (Sec. 107.)

PROBLEMS

143. How many square feet in a cement sidewalk 6 ft. wide and 180 ft. long?

144. A house is approximately 22' x 30' X18' high. Allowing 30 sq.yds for gables and dormers, how many square yards of painting surface are there on the house?

145. If a gallon of paint will cover 100 sq.yds. two coats, how many gallons of paint will be required for the above house?

146. If a silo is 18' across, how many feet are there around it?

147. A farmer can measure the distance around his silo with a tape, but he cannot measure across it. He finds that the distance around is 501'. Tell him the distance across it.

148. How many cubic feet does a bin 6 ft. square and 8 ft. high contain? How many bushels?

149. How many barrels of water will a cistern that is 4 ft. square and 8 ft. high hold?

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150. A testing tank shown in Fig. 35 is built of concrete. It is 6 ft. deep, 14 ft. wide and 25 ft. long. How many barrels of water will it hold?

151. If water weighs 627 pounds per cubic foot, how much will the water in the above-mentioned tank weigh?

152. How much will a stick of green white oak 12''x12''X 10' weigh? Add one-fourth to the dry weight to allow for moisture.

153. How much will 500 pieces 2"x4"X16' seasoned Northern pine scantlings weigh?

154. If the freight in carload lots from St. Louis to Des Moines is 22€ per hundred pounds, what will the charges on a load of red oak which measures 8' 4" wide, 32 ft. long and 6. ft. high when closely piled? Figure 38 pounds per cubic foot.

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155. A carload of common hard brick measures 8' 4" wide, 5 ft. high and 30 ft. long. What is the weight of the load?

156. A certain concrete chimney contains about 1 cu.yds. of concrete for every foot of height. How much will a stack 150 ft. high weigh in tons?

157. What must be the size of the footing for the above-mentioned chimney if it is to be placed on gravel and coarse sand well cemented?

158. A chimney for a residence is 35' high and is made of common hard brick of the dimensions shown in Fig. 36. What must be the size of the footings allowing į ton to the square foot?

159. A concrete retaining wall is 18" wide, 8' high and 60' long. A1:3 : 5 mixture is used. How many barrels

of cement and cubic yards of sand and gravel will be required?

160. The walls of the testing FIG. 36.-Chimney. tank shown in Fig. 35 are 9'' thick and the floor is 12" thick. What will be the weight of the tank when it is full of water? Whai will be the pressure per square foot of bearing surface?

161. A cement sidewalk is 6' wide, 180' long and 4" in total thickness. The base is a 1:3 :5 mixture and the top coat, which is 1" thick, is a 1:1} mixture. How much cement, sand and gravel will be required?

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CHAPTER XI

POWERS. ROOTS. RIGHT TRIANGLES. AREA OF

CIRCLES. CAPACITY OF TANKS AND CISTERNS

108. Powers. It is sometimes convenient and necessary to multiply a number by itself one or more times. This is performed just like any ordinary multiplication, but we have a special name for the product. When a number is multiplied by itself one or more times we call the resulting produet the power of the number. The number which is used as a factor is call the base.

Thus in the expression, 2X2=4, we have raised 2 to second power. The base is 2 and 4 is the power. Again in the expression 2X2X2=8, we have raised 2 to the third power. Instead of writing 2X2X2=8, we may shorten it by writing 23 = 8. The small figure above and to the right of 2 indicates how many times 2 is to be used as a factor.

109. Exponents. The exponent of a power is a small figure placed above and to the right of the base to indicate how many times it is to be used as a factor to get the power. The second power of a number is called the square of the number.

The third power of a number is called the cube of that number. The powers above the third have no special names. They are simply called the fourth power, the eighth power, etc. The process of finding the powers of numbers is called involution.

Explanation. To find the square of a number we must use it twice as a factor. 25 times 25 is 625. Example. Raise 9 to the fifth power.

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Explanation. To raise 9 to the fifth power means that we must use 9 as a factor five times.

To raise number to a given power we must use it as a factor as many times as indicated by the exponent.

110. Powers of Common Fractions. To raise a common fraction to a given power we raise the numerator to the