Chapter 11: Surface Areas and Volumes

Volumes

Formulas

ShapeVolume
Cuboidl×b×hl \times b \times h
Cubea3a^3
Cylinderπr2h\pi r^2 h
Cone13πr2h\frac{1}{3}\pi r^2 h
Sphere43πr3\frac{4}{3}\pi r^3
Hemisphere23πr3\frac{2}{3}\pi r^3

Key Relations

  • Volume of cone = 13\frac{1}{3} × Volume of cylinder
  • 3 cones = 1 cylinder (same r, h)

Example

Cylinder: r=7r = 7 cm, h=10h = 10 cm

Volume = πr2h\pi r^2 h = 227×49×10\frac{22}{7} \times 49 \times 10 = 15401540 cm³