Volume for 5th Grade: Counting Unit Cubes and Formulas
Volume is the amount of space inside a three-dimensional shape. In Grade 5, students find the volume of rectangular prisms (including cubes) using the formula length × width × height. Volume is measured in cubic units—cubic centimeters (cm³), cubic meters (m³), cubic feet (ft³), etc. Volume is used when filling a box, measuring storage space, or determining how much a container holds.
For a rectangular prism, the volume is length × width × height because we count how many unit cubes fit inside—if the dimensions are 5 cm by 3 cm by 2 cm, we have 5 × 3 = 15 cubes per layer and 2 layers, so 15 × 2 = 30 cubic cm. For a cube with side length s, volume = s × s × s = s³.
DETAILED EXPLANATION
Volume of rectangular prism: \(V = l \times w \times h\), where l = length, w = width, h = height.
Volume of cube: \(V = s^3\), where s = side length (since length = width = height = s).
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Units: Volume is measured in cubic units (cm³, m³, ft³, etc.).
WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS
Example 1
A box is 5 cm long, 3 cm wide, and 2 cm high. Find the volume.
Solutions:
Step 1: The volume of a rectangular prism is \(V = \text{length} \times \text{width} \times \text{height}\).
Step 2: Substitute: \(V = 5 \times 3 \times 2 = 30\).
Step 3: The volume is 30 cubic centimeters (or 30 cm³).
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Answer: 30 cubic cm (or 30 cm³)
Example 2
A cube has side length 4 m. Find the volume.
Solutions:
Step 1: A cube has equal length, width, and height. Volume = side × side × side = s³.
Step 2: Substitute: \(V = 4 \times 4 \times 4 = 64\).
Step 3: The volume is 64 cubic meters.
Answer: 64 cubic meters (or 64 m³)
Example 3
A storage bin is 10 ft by 6 ft by 4 ft. How many cubic feet of space does it hold?
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Solutions:
Step 1: \(V = \text{length} \times \text{width} \times \text{height}\).
Step 2: \(V = 10 \times 6 \times 4 = 240\).
Step 3: The bin holds 240 cubic feet of space.
Answer: 240 cubic feet
Example 4
A rectangular tank is 12 cm long, 5 cm wide, and 8 cm high. Find its volume.
Solutions:
Step 1: \(V = 12 \times 5 \times 8\).
Step 2: \(12 \times 5 = 60\); \(60 \times 8 = 480\).
Answer: 480 cm³
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