Geometry · Grades 9 to 10
Volume and surface area
Measure the space inside and the surface of a prism.
The idea
The volume of a rectangular prism is the space it fills: length times width times height.
Surface area is the total area of all six faces. Each pair of opposite faces matches, so surface area is 2(lw + lh + wh).
Worked examples
- How to Find the Volume of a Rectangular Prism Find the volume of a box 4 by 3 by 5. Three steps with V = lwh, the cubic units, and the add-or-multiply mistakes to avoid.
- Find the Surface Area of a Rectangular Prism Find the surface area of a box 4 by 3 by 5. Four steps with 2(lw + lh + wh), the three face pairs, and the mistakes to avoid.
- How to Find the Volume and Surface Area of a Cube A cube with side 4 has volume 64 and surface area 96. Four steps with V = s^3 and SA = 6s^2, and the cubed-versus-squared mistakes.
Practice this topic
3 problems with answers.