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APEX Calculus

Section B.4 Areas and Volumes

Triangles
  • \(\displaystyle h=a\sin \theta\)
  • Area = \(\frac12bh\)
  • 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 = \(Ah\)