Mensuration Formulas

Circle

Variables: R = radius
  1. Circumference: \[ C = 2\pi R \]
  2. Area: \[ A = \pi R^2 \]

Sphere

Variables: R = radius
  1. Surface area: \[ A = 4\pi R^2 \]
  2. Volume: \[ V = \frac{4}{3}\pi R^3 \]

Cylinder

Variables: R = radius, h = height
  1. Curved surface area: \[ A_{curved} = 2\pi R h \]
  2. Total surface area: \[ A_{total} = 2\pi R (R + h) \]
  3. Volume: \[ V = \pi R^2 h \]

Cone

Variables: R = radius, h = height, l = slant height
  1. Lateral surface area: \[ A_{lateral} = \pi R l \]
  2. Total surface area: \[ A_{total} = \pi R (R + l) \]
  3. Volume: \[ V = \frac{1}{3}\pi R^2 h \]

Ellipse

Variables: a = semi-major axis, b = semi-minor axis
a b
  1. Circumference: \[ C = 2\pi \sqrt{\frac{a^2 + b^2}{2}} \]
  2. Area: \[ A = \pi a b \]

Trapezoid

Variables: a = length of first parallel side, b = length of second parallel side, h = height (distance between parallel sides)
a b h
  1. Area: \[ A = \frac{1}{2} \times (a + b) \times h \]