a • .] 2. A when a= 14, b = 20 when = 3.1416, r = 10 1 4 when m= 18, v=4 9. F= f . C + 32 when C= 20 10. C= _ (F -32) when F= 50 m Exercise Evaluate in the following, using in each case the accompanying data : 1. V=a.b.c when a = 14, b 12, c= = 6 2. A ET p2 when a = 3.1416, r = - 16 3. A = 772 when 3.142, r= 14 22 4. A= d=6 T = when a = = SE 5. S=1.g.t2 when g= = 32.2, t = 6.5 6. a= V2 - 12 when c=13, b 5 7. A=V8(8 – a) (8 – b)(8 - c) when a = 8,6 = 10, c = 12, a+b+c 2 3.1416, d=4 22 when a = 3 7 10. A=(R2 - y2) when R = 14, r= 12, = 3.1416 when # = p=5 Exercise 1. In the formula s = 1 gt?, assume g=32, and assign to t successive values from 0 to 10, and tabulate the corresponding values of s. 2. In the formula C = ( (F - 32), assign to F successive values from 60 to 70 and arrange in tabular form the corresponding values for C. 3. In the formula F= $C + 32, assign to C successive values from 20 to 30 and arrange in tabular form the corresponding values for F. 4. Make a table for corresponding values of A and r by assigning to r successive values from 0 to 10, in the formula A πι2. . 5. Tabulate the resulting values of A obtained by assigning to d successive values from 1 to 10 in the formula A= πd? Exercise Express as formulas the following rules : 1. To find the area of a circle, multiply the square of the diameter by .7854. 2. To find the area of a sphere, multiply the square of the diameter by 3.1416. 3. To find the volume of a sphere, multiply the cube of the diameter by .5236. 4. To find the volume of a spherical segment, add the square of its altitude to three times the square of the radius of the base; multiply this sum by the altitude, and the product by .5236. 5. To find the volume of a cylinder, multiply the area of the base by the altitude. SPHERICAL SEGMENT 6. To find the volume of a cone or pyramid, multiply the area of the base by one third the altitude. 7. To find the volume of a frustum of a cone or pyramid : To the sum of the areas of the bases add the square root of their product and multiply the sum by one third the altitude of the frustum, 100 212• 90 80 70 140° 8. To find the area of an ellipse, multiply the product of the diameters by .7854. 9. To find the area of an equilateral triangle, multiply the square of one side by .433. 10. To find the diameter of a circle, multiply the circumference by .3183. 11. To find the radius of a circle, multiply the circumference by .15915. 12. To find the side of a square inscribed in a circle, multiply the diameter by .7071. 13. To find the side of a square inscribed in a circle, multiply the circumference by .2251. 14. To find the side of a square equal in area to that of a given circle, multiply the 194 diameter by .8862. 176 15. To find the side of a square equal in 188 area to that of a given circle, multiply the cir 122° cumference by .2821. 104° 16. To find the horse power of an engine, multiply together the mean effective pressure on the piston in pounds per square inch, the length of the stroke in feet, the area of the 32 piston in square inches, and the number of strokes per minute; divide this product by 33,000. 17. To convert Centigrade reading to CENTIGRADE AND Fahrenheit, multiply by 1.8 and add 32. 18. To convert Fahrenheit reading to Centi THERMOMETERS grade, subtract 32 and multiply by .56. 19. To find the area of a triangle when the sides are given, multiply in succession half the sum of the sides by the three remainders obtained by subtracting each side separately from the half-sum of the sides, and take the square root of this product. 80 80 88 20 68 10 50 -10 -17.78° FAHRENHEIT 1. If three fourths of the weight of potatoes is water, and if a bushel of potatoes weighs 60 pounds, what is the weight of water in 300 bushels of potatoes ? What is the weight of that part which is not water? 2. If wheat weighs 60 pounds per bushel, and the average yield is 28 bushels per acre, what will be the weight of the wheat grown on a field of 40 acres ? 3. If during a rainstorm 0.72 in. of rain fell on an 80-acre field, how many cubic inches of water fell on 1 square foot ? 1 square rod ? on 1 acre ? on the whole field ? 4. If a kitchen poorly arranged requires the housekeeper to take 100 more steps, 20 inches to a step, each day in preparing the meals, than she would in a well-arranged kitchen, how many miles of unnecessary travel does this amount to in the course of a year ? on |