Volume and Surface Area

Prisms and cylinders

Rectangular prism

V = l w h S A = 2 (l w + l h + w h)

Rectangular prism, space diagonal

d = \sqrt{l^{2} + w^{2} + h^{2}}

Cube

V = s^{3} S A = 6 s^{2} d = s \sqrt{3}

Any right prism

V = B h L A = P h S A = 2 B + P h

B base area, P base perimeter

Cylinder

V = π r^{2} h L A = 2 π r h S A = 2 π r^{2} + 2 π r h

Pyramid

V = \frac{1}{3} B h L A = \frac{1}{2} P l S A = B + \frac{1}{2} P l

l slant height

Cone

V = \frac{1}{3} π r^{2} h L A = π r l S A = π r^{2} + π r l

l = √(r² + h²)

Frustum of a cone

V = \frac{1}{3} π h (R^{2} + R r + r^{2}) L A = π (R + r) l

Sphere

V = \frac{4}{3} π r^{3} S A = 4 π r^{2}

Hemisphere

V = \frac{2}{3} π r^{3} S A = 3 π r^{2}

SA includes the flat circle

Euler's formula

V - E + F = 2

vertices, edges, faces

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