Section B.4 Areas and Volumes
Triangles
\(\displaystyle h=a\sin \theta\)
Area = \(\frac12bh\)
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Law of Cosines:
\begin{equation*} c^2=a^2+b^2-2ab\cos \theta \end{equation*}
Right Circular Cone
Volume = \(\frac 13 \pi r^2h\)
Surface Area = \(\pi r\sqrt{r^2+h^2} +\pi r^2\)
Parallelograms
Area = \(bh\)
Right Circular Cylinder
Volume = \(\pi r^2h\)
Surface Area = \(2\pi rh +2\pi r^2\)
Trapezoids
Area = \(\frac12(a+b)h\)
Sphere
Volume = \(\frac43\pi r^3\)
Surface Area =\(4\pi r^2\)
Circles
Area = \(\pi r^2\)
Circumference = \(2\pi r\)
General Cone
Area of Base = \(A\)
Volume = \(\frac13Ah\)
Sectors of Circles
\(\theta\) in radians
Area = \(\frac12\theta r^2\)
\(\displaystyle s=r\theta\)
General Right Cylinder
Area of Base = \(A\)
Volume = \(Ah\)
