The Big Difference
Around vs cover vs fill
Perimeter
Counts the outside path only. It is a length, so the unit is plain.
P = 2L + 2W
Unit: feet
Area
Counts how many unit squares cover a flat surface. It is two-dimensional.
A = L x W
Unit: square feet
Volume
Counts how many unit cubes fill a 3D space. It needs length, width, and height.
V = L x W x H
Unit: cubic feet
Try the Same Rectangle
Interactive model
5 ft wide
4 ft long
Fence
18 ft
around the edge
Grass
20 sq ft
cover the floor
Box
60 cu ft
fill with cubes
Why Volume Needs Height
Layer model
60
Area tells you how many squares are in one flat layer. Volume asks how many layers of that same floor fit inside the box.
20 square feet per layer x 3 layers = 60 cubic feet
A box that is only one layer tall has volume too. Height tells how many layers there are.
Pick the Right Idea
Quick check
You are putting ribbon around a poster. What do you need?
You are buying carpet for a room. What do you need?
You are filling a storage bin with blocks. What do you need?