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The JPCHEMICAL
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| Basics in Mathematics |
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Simple Geometric Mathematics CIRCLE Area of a Circle The area of a circle is p ? r2 or p ? r ? r, where r is the length of its radius. p is a number that is approximately 3.14159. Radius: r Diameter: d Circumference: C Area: K d = 2r C = 2 p r = p d K = p r2 = p d2/4 C = 2 p r K = p d2 /4 Area on the sphere The area of a sphere of radius R is 4 R . A great circle divides the sphere into two congruent hemispheres. Each of these will have area 2 R . Another great circle, which meets the first at right angles, divides the sphere into four congruent lunes, each with area R . Triangle Consider a triangle with base length b and height h. The area of the triangle is 1/2 ? b ? h. Parallelogram The area of a parallelogram is b ? h, where b is the length of the base of the parallelogram, and h is the corresponding height. To picture this, consider the parallelogram below: Trapezoid If a and b are the lengths of the two parallel bases of a trapezoid, and h is its height, the area of the trapezoid is 1/2 ? h ? (a + b) . Cylinders If r is the radius of the base and h is the altitude, the area is 2 rh, and the volume is r h. Conicals |
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