Theory Exercises

Metric Prefixes

PrefixSymbolValue
gigaG10⁹
megaM10⁶
kilok10³
hectoh10²
decada10¹
(unit)1
decid10⁻¹
centic10⁻²
millim10⁻³
microμ10⁻⁶
nanon10⁻⁹
picop10⁻¹²

Essential Unit Equalities

Volume
1 kL = 1 m³1 L = 1 dm³
1 mL = 1 cm³

Volume Formulas for Geometric Objects

ObjectFormulaVariables
Cube\(V = a^3\)\(a\) = side length
Rectangular Prism\(V = l \times w \times h\)\(l\) = length, \(w\) = width, \(h\) = height
Sphere\(V = \frac{4}{3}pi r^3\)\(r\) = radius
Cylinder\(V =pi r^2 h\)\(r\) = radius, \(h\) = height
Cone\(V = \frac{1}{3}pi r^2 h\)\(r\) = radius, \(h\) = height
Triangular Prism\(V = \frac{1}{2} \times b \times h \times l\)\(b\) = base, \(h\) = height of triangle, \(l\) = length
Pyramid\(V = \frac{1}{3} \times A \times h\)\(A\) = base area, \(h\) = height

Material Densities

MaterialDensity (kg/m³)
Gold19 300
Silver10 490
Lead11 340
Copper8 960
Brass8 600
Aluminum2 700
Polyethylene900
Oak (wood)700
Cork250