Geometric Formulas

Volume Formulas for Prisms and Rectangular Solids

• Rectangular Prism:

  • Formula 1: $V = l \times w \times h$
  • Formula 2: $V = L \times W \times H$
  • Variable Definitions:
  • $V$ = Volume of the rectangular prism
  • $L$ or $l$ = Length of the prism base
  • $W$ or $w$ = Width of the prism base
  • $H$ or $h$ = Perpendicular height of the prism

• Triangular Prism:

  • Formula: $V = \frac{1}{2} b h l$
  • Variable Definitions:
  • $V$ = Volume of the triangular prism
  • $b$ = Base length of the triangular cross-section
  • $h$ = Height of the triangular face
  • $l$ = Length or depth extending between the triangular faces

Volume Formulas for Circular and Spherical Solids

• Cylinder:

  • Formula: $V = \pi r^2 h$
  • Variable Definitions:
  • $V$ = Volume of the cylinder
  • $\pi$ = Mathematical constant Pi
  • $r$ = Radius of the circular base
  • $h$ = Height of the cylinder

• Sphere:

  • Formula: $V = \frac{4}{3} \pi r^3$
  • Variable Definitions:
  • $V$ = Volume of the sphere
  • $\pi$ = Mathematical constant Pi
  • $r$ = Radius of the sphere

• Hemisphere:

  • Formula: $V = \frac{2}{3} \pi r^3$
  • Variable Definitions:
  • $V$ = Volume of the hemisphere
  • $\pi$ = Mathematical constant Pi
  • $r$ = Radius of the hemisphere

Volume Formulas for Pyramids and Cones

• Pyramid:

  • Formula: $V = \frac{1}{3} b \times h$
  • Variable Definitions:
  • $V$ = Volume of the pyramid
  • $b$ = Base area or base measurement
  • $h$ = Perpendicular height from the base to the top apex

• Cone:

  • Formula: $V = \frac{1}{3} \pi r^2 h$
  • Variable Definitions:
  • $V$ = Volume of the cone
  • $\pi$ = Mathematical constant Pi
  • $r$ = Radius of the circular base
  • $h$ = Perpendicular height from the circular base to the apex