8th Grade Math

Algebra foundations, geometry, and mathematical modeling for eighth grade students.

Linear Equations and ExpressionsFunctions and GraphsIntro to Geometry: Angles and Shapes
Systems of EquationsPythagorean TheoremVolume and Surface Area of 3D Shapes
Budgeting and Saving with AlgebraGeometry in Construction and DesignModeling and Interpreting Data
Breaking Down Word ProblemsChecking Your Work and Estimating
Linear Equations and...Functions and GraphsIntro to Geometry: A...Systems of EquationsPythagorean TheoremVolume and Surface A...Budgeting and Saving...Geometry in Construc...Modeling and Interpr...Breaking Down Word P...Checking Your Work a...
Advanced Topics

Volume and Surface Area of 3D Shapes

Understanding 3D Shapes

Three-dimensional (3D) shapes have length, width, and height. Common 3D shapes include cubes, rectangular prisms, cylinders, and spheres.

Volume

Volume is the amount of space inside a 3D shape.

  • Rectangular prism: \(V = l \times w \times h\)
  • Cylinder: \(V = \pi r^2 h\)

Surface Area

Surface area is the total area of all the faces on a 3D object.

  • Cube: \(SA = 6s^2\)
  • Cylinder: \(SA = 2\pi r^2 + 2\pi rh\)

Why Is This Useful?

Knowing volume helps you figure out how much water a tank can hold. Surface area tells you how much material covers a box.

Examples

  • A box 2 ft by 3 ft by 4 ft has a volume of 24 cubic feet.

  • A can with radius 2 cm and height 5 cm has surface area \(2\pi(2^2) + 2\pi(2)(5) = 8\pi + 20\pi = 28\pi\) square cm.

In a Nutshell

Volume and surface area help us measure and build 3D objects.

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Budgeting and Saving with Algebra