Circumference of a Circle

O=2⋅π⋅rO = 2\cdot\pi\cdot r

Area of a Circle

A=π⋅r2A = \pi\cdot r^2

Surface Area of a Ball

A=4⋅π⋅r2A = 4\cdot\pi\cdot r^2

Volume of a Ball

V=43⋅π⋅r3V = \frac 43\cdot\pi\cdot r^3

Volume of a Cylinder (base times height)

V=A⋅hV = A\cdot h

Logarithms

log⁡(a⋅b)=log⁡(a)+log⁡(b)\log(a\cdot b) = \log(a) + \log(b)
log⁡(ac)=c⋅log⁡(a)\log(a^c) = c\cdot\log(a)
lg⁡(a)=d  ⟹  a=10d\lg(a) = d \implies a = 10^d
ln⁡(a)=d  ⟹  a=ed\ln(a) = d \implies a = e^d