Surface Area and Volume
Lessons in this chapter
About Surface Area and Volume
Surface Area and Volume separates two measurements of a solid that are easy to confuse: the skin of it and the space inside it.
Identify Three-Dimensional Figures sorts the solids by structure. A prism has two identical parallel bases joined by rectangles; a pyramid has one base and triangular faces meeting at an apex. The names describe how the faces are arranged, not just what the solid looks like.
Find the Surface Area of Prisms is best approached through the net, the flattened solid. Unfolding a prism turns a 3D problem into a set of 2D areas to add, which uses the formulas from the previous chapter and makes it clear why surface area is measured in square units.
Find the Surface Area of Pyramids does the same with triangular faces, where the slant height rather than the vertical height is what the triangle area needs. Mixing those two heights is the usual error.
Find the Volume of Rectangular Prisms returns to length times width times height from 5th grade, now alongside surface area so the contrast is explicit: surface area is square units and covers the outside, volume is cubic units and fills the inside.
All four lessons in Surface Area and Volume open as 6th grade math worksheets in the page. Find the Surface Area of Prisms, Find the Surface Area of Pyramids and Find the Volume of Rectangular Prisms each give math problems worked one at a time and scored as you go, which is usually where the slant height and vertical height mix-up surfaces. Free to try, with no login needed for your first 3.
Frequently asked questions
Identify Three-Dimensional Figures sorts solids by how their faces are arranged, a prism having two identical parallel bases and a pyramid one base with triangular faces meeting at a point. Find the Surface Area of Prisms then works through the net, the flattened solid, which turns a three-dimensional problem into a set of flat areas to add, and Find the Surface Area of Pyramids does the same with triangles, where the slant height rather than the vertical height is what the triangle needs. Find the Volume of Rectangular Prisms sits alongside them on purpose, so the contrast stays explicit: surface area covers the outside in square units, volume fills the inside in cubic units. The chapter sits in the Common Core domain Geometry (6.G).
Surface area is the total area of the outside, measured in square units. Volume is the space inside, measured in cubic units. One wraps the solid, the other fills it.
A flattened solid, unfolded so all its faces lie flat. It turns a surface area problem into a set of 2D areas to add, which is the easiest way to get it right.
A prism has two identical parallel bases joined by rectangles. A pyramid has one base and triangular faces meeting at a single point.
The height of a triangular face of a pyramid, measured along the face. It is not the vertical height of the pyramid, and confusing the two is the usual error.
Length times width times height. It counts the unit cubes that fit inside, which is why the answer is in cubic units.