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Solids (Volume and Surface Area) Formulas and Notes

Cylinder

cylinder


Volume \displaystyle = \pi r^{2} h

Surface Area \displaystyle = 2 \pi r^{2} + 2 \pi r h

Cone

cone


Volume \displaystyle = \frac{ \pi r^{2} h}{3}

Surface Area \displaystyle = \pi r^{2} + \pi r l

Sphere

sphere


Volume \displaystyle = \frac{4 \pi r^{3} }{3}

Surface Area \displaystyle = 4 \pi r^{2}

Hemisphere

hemisphere


Volume \displaystyle = \frac{2 \pi r^{3} }{3}

Surface Area \displaystyle = 2 \pi r^{2} + \pi r^{2} = 3 \pi r ^{2}

Pyramid

pyramid


Volume \displaystyle = \frac{ lbh }{3}

Surface Area \displaystyle = lb + 2bc

Cube

cube


Volume \displaystyle = s^{3}

Surface Area \displaystyle = 6s^{2}

Cuboid/Rectangular Prism

cuboid. rectangular prism


Volume \displaystyle = lbh

Surface Area \displaystyle = 2bh + 2bl + 2lh

Triangular Prism

trianglular prism


Volume \displaystyle = \frac{ abc }{2}

Surface Area \displaystyle = ab + 3(ac)

Parallelepiped

Parallelepiped


Volume \displaystyle = \left| ( \bar{a} \times \bar{b} ) \cdot \bar{c} \right|


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