1A rectangular prism is always three pairs of faces
The six faces that make up a box split into three pairs of opposite faces: top-bottom, front-back, and side-side. Each pair of opposite faces is exactly the same size and shape.
So instead of adding up all six faces one by one, you only need to find three different areas and double them.
2Surface area = the sum of all three pairs
If length is a, width is b, and height is h, here's how you find the surface area.
For a box with length 4, width 3, and height 2: 2×(4×3 + 4×2 + 3×2) = 2×(12+8+6) = 52.
On the activity page, press "View as net" and watch the box unfold — you can count exactly how many of each of these three pairs there really are.
3Volume = length × width × height
Volume tells you how many cube-shaped blocks would fit inside the box. Think of laying down a length × width layer of blocks on the floor, then stacking that same layer up to the height.
For length 4, width 3, and height 2: one floor layer holds 4×3=12 blocks, and there are 2 such layers, so 12×2 = 24.
4Surface area and volume change differently
Double the length, width, and height all together, and surface area grows by 4 times (squared), while volume grows by 8 times (cubed). That's because surface area measures a "face," which multiplies two lengths together, while volume fills "space," which multiplies three lengths together.
When length, width, and height are all equal, you get a cube. In that case, surface area simplifies to 6×(side)², and volume simplifies to (side)³.
5Try this
- Change just one side. Double only the height and compare how much surface area and volume each grow by.
- Turn it into a cube. Make length, width, and height all equal and see how the surface area and volume formulas simplify.
- Count the net. Among the six unfolded faces, pair up the ones that match in size, and check that they line up with the formula's three pairs.