Grade 5 Mathematics
Volume measures how much space a 3D shape takes up - how many unit cubes fit inside.
We measure volume in CUBIC units (like cubic centimeters, cubic inches, or cubic feet) because we're filling the shape with cubes!
V = l x w x h
Volume = length x width x height
You can also use: V = B x h (Base area x height)
This prism is made of unit cubes. What is its volume?
Width = 3 (going back)
Count the bottom layer: 4 x 3 = 12 cubes in one layer
Count the layers: 2 layers (the height is 2)
Multiply: 12 cubes x 2 layers = 24 cubic units
Using the formula: V = 4 x 3 x 2 = 24 cubic units
Problem: A box is 6 inches long, 4 inches wide, and 5 inches tall. What is the volume?
V = l x w x h
V = 6 x 4 x 5
V = 120 cubic inches
WRONG: "The volume is 6 x 4 = 24 square inches" (That's only the BASE AREA!)
RIGHT: Volume needs ALL THREE dimensions and uses CUBIC units.
V = 6 x 4 x 5 = 120 cubic inches
Sometimes shapes are made of TWO rectangular prisms. Find each volume and ADD!
Break it into parts: Green prism (top) + Yellow prism (bottom)
Find each volume:
Green: 3 x 2 x 2 = 12 cubic units
Yellow: 6 x 2 x 2 = 24 cubic units
Add them: 12 + 24 = 36 cubic units
1. A rectangular prism is 5 cm long, 3 cm wide, and 4 cm tall. What is the volume?
V = _____ x _____ x _____ = _________ cubic cm
2. A shipping box has a volume of 72 cubic inches. The length is 6 inches and the width is 4 inches. What is the height?
V = l x w x h 72 = 6 x 4 x _____ Height = _________ inches
3. An L-shaped figure is made of two rectangular prisms:
- Prism A: 4 ft x 2 ft x 3 ft
- Prism B: 5 ft x 2 ft x 2 ft
Volume of A = _________ Volume of B = _________ Total = _________ cubic ft