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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 = \(Ah\)

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