General Formulas

Here are some common simple geometric formulas useful in estimating sizes, quantities and amounts:

Volume of a cube in cubic yards

cuyd’s = (length’ x width’ x height’) / 27
Why 27?   Because 3’ x 3’ x 3’ = 27 cuft = 1 cuyd

Area of a parallelogram

area =  a x b

Area of a trapezoid

area = ((a + b) / 2 ) x c

Hypotenuse of a right triangle

Area of any triangle

area = (a x b) / 2

pi

What exactly is pi?

Why is it 3.1416?

If you take any circle, measure its circumference, measure its diameter, and divide the circle’s circumference by its diameter, the answer is always 3.1416.  This ratio of the circumference to the diameter is always the same, regardless of the size of the circle or its units of measure.

Volume of a cylinder

volume = ( pi  / 4) x a² x b and volume = pi x a/2 x a/2 x b

Area of a circle

A circle’s area can be determined by using either the radius or the diameter
area = pi a²

area = 0.785 b²

Circumference of a circle

circumference =  pi b

Volume of a pyramid

volume = ( a x b x c ) / 3

Volume of a frustum of a pyramid

Volume of a cone

volume = ( pi / 3 ) x b² x c

Volume of a frustum of a cone

volume = (pi / 12) x c x ( a² + (a x b) + b² )

Frustum's surface area

Tangent Examples:

tangent 30° = 0.57735
tangent 35° = 0.70021
tangent 40° = 0.83910
tangent 45° = 1.00000
tangent 50° = 1.19175
tangent 55° = 1.42815
tangent 60° = 1.73205
tangent 65° = 2.14451
tangent 70° = 2.74748

Volume of a sphere

volume =  ( pi / 6 ) x a³

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