Math Notes PDF

# MATH NOTES ## Units of Measurement ### Length * **SI:** m, cm, km, mm * **Imperial:** in, ft, yd, mi ### Weight * **SI:** g, kg, mg, etc * **Imperial:** oz, lb, ton ### Time * **SI:** s, min, hour, day, week, month, year ## Conversion * **Example:** 3 g = 0.003 kg = 300 cg ## Rectangular...

# MATH NOTES ## Units of Measurement ### Length * **SI:** m, cm, km, mm * **Imperial:** in, ft, yd, mi ### Weight * **SI:** g, kg, mg, etc * **Imperial:** oz, lb, ton ### Time * **SI:** s, min, hour, day, week, month, year ## Conversion * **Example:** 3 g = 0.003 kg = 300 cg ## Rectangular Pyramid ### Volume * **Formula:** $V = \frac{lwh}{3}$ where: * l = length * w = width * h = height * **Example:** * l = 3, w = 4, h = 5 * $V = \frac{3 \times 4 \times 5}{3} = 20 cm^3$ ### Height * **Formula:** $h = \frac{3V}{lw}$ * **Example:** * l = 3, w = 4, V = 20 * $h = \frac{3 \times 20}{3 \times 4} = 5$ ### Length * **Formula:** $l = \frac{3V}{wh}$ * **Example:** * w = 3, h = 4, V = 20 * $l = \frac{3 \times 20}{3 \times 4} = 5$ ### Width * **Formula:** $w = \frac{3V}{lh}$ * **Example:** * l = 3, h = 4, V = 20 * $w = \frac{3 \times 20}{3 \times 4} = 5$ ## Square Pyramid ### Volume * **Formula:** $V = \frac{s^2h}{3}$ where: * s = side length * h = height * **Example:** * s = 4, h = 3 * $V = \frac{4^2 \times 3}{3} = 16 cm^3$ * $s = \sqrt[2]{\frac{3V}{h}} = \sqrt[2]{\frac{3 \times 16}{3}} = \sqrt[2]{16} = 4 cm$ ### Height * **Formula:** $h = \frac{3V}{s^2}$ * **Example:** * s = 4, V = 36 * $h = \frac{3 \times 36}{4^2} = \frac{108}{16} = 6.75 cm$ ## Cylinder ### Volume * **Formula:** $V = \pi r^2 h$ where: * r = radius * h = height ### Height * **Formula:** $h = \frac{V}{\pi r^2}$ * **Example:** * $V = 113.10$ * $r = \sqrt[2]\frac{113.10}{\pi \times (3^2)} = \sqrt[2]{\frac{113.10}{28.27}} = \sqrt[2]{4} = 2$ * $h = \frac{113.10}{\pi \times (2^2)} = \frac{113.10}{12.56} = 9$ ## Fractions/Decimals * $\frac{1}{10.001} = 0.1$ * $\frac{1}{3} = 0.333...$ * $\sqrt[2] {3} = 1.732...$ * $\sqrt[2] {16} = 4$ * $\sqrt[2] {0.01} = 0.1$