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Relative to a Circle

  • To find Circumference - Multiply the diameter by 3.1416; or, divide diameter by 0.3183.
  • To find Diameter - Multiply the circumference by 0.3183; or, divide circumference by 3.1416.
  • To find Radius - Multiply the circumference by 0.15915; or, divide circumference by 6.28318; or, divide diameter by 2.
  • To find the Side of a Square to be Inscribed in a Circle - Multiply diameter by 7071; or, multiply the circumference by 0.2251; or, divide the circumference by 4.4428.
  • To find the Side of a Square to equal the Area of a Circle - Multiply the diameter by 0.8862; or, divide diameter by 1.1284; or, multiply the circumference by 0.2821; or, divide the circumference by 3.545.
  • To find the Area of a Circle - Multiply the circumference by one-quarter of the diameter; or, multiply the square of the diameter by 0.7854; or, multiply the square of the circumference by 0.7958; or, multiply the square of one-half the diameter by 3.1416. Doubling the diameter of a circle increases the area 4 times.

Relative to a Square

  • A side multiplied by 1.412 equals the diameter of a circle which will circumscribe the given square.
  • A side multiplied by 4.443 equals the circumference of its circumscribing circle.
  • A side multiplied by 1.1284 equals the diameter of a circle equal in area to that given square.
  • A side multiplied by 3.545 equals the circumference of an equal circle.
  • To find the Area of an Ellipse-Multiply the product of its axes by .7854; or, multiply the product of its semi-axes by 3.14159.

Relative to Other Geometrical Forms

To find:

  • Contents of a cylinder = area of end x length.
  • Contents of a wedge = area of triangular base x altitude.
  • Surface of a cylinder = length x circumference plus area of both ends.
  • Surface of a sphere = diameter squared x 3.1416; or, diameter x circumference.
  • Contents of a sphere = diameter cubed x 0.5236.
  • Contents of a pyramid or cone, right or oblique, regular or irregular = area of base x one-third of the altitude.
  • Area of a triangle = base x one-half the altitude.
  • Area of a parallelogram = base x altitude.
  • Area of a trapezoid = altitude x one-half the sum of parallel sides.

To Find the Capacity of a Tank in Gallons

1. All measurements must be reduced to inches.

  • For rectangular tanks, multiply the length by the width by the depth.
  • For cylindrical tanks, multiply the length by the square of the diameter by .7854.
  • For elliptical section tanks, multiply the length by the short diameter by the long diameter by .0339.

2. Divide the result of any of the above calculations by 231, which is the number of cubic inches in a gallon; the result is the capacity of the tank in gallons.