Counting Cubes
A model is built using 15 unit cubes. What is its volume?
15 cubic units
What formula is always used to calculate the volume of a rectangular prism?
Volume = length × width × height (V = l × w × h)
A prism has a volume of 48 cubic units. The base measures 4 × 3. What is the missing height?
Volume ÷ base = 48 ÷ 12 = 4 units
Write an expression for the volume of a prism with sides 2, 3, and 6.
Expression: 2 × 3 × 6
A fish tank measures 2 ft × 3 ft × 1 ft. How many cubic feet of water fit inside?
2 × 3 × 1 = 6 ft³
A prism made of 40 unit cubes has what volume?
40 cubic units
A prism has dimensions 2 × 5 × 4. What is its volume?
2 × 5 × 4 = 40 cubic units
A prism has a base of 8 × 2 and a height of 5. What is its volume?
8 × 2 × 5 = 80 cubic units
Which expressions equal the volume of a prism with dimensions 4, 5, and 2: (4×5)×2 or 4+5+2?
Correct: (4×5)×2 = 40; 4+5+2 = 11 (not volume). Answer: (4×5)×2
A sandbox is 4 m long, 2 m wide, and 1 m deep. What is its volume?
4 × 2 × 1 = 8 m³
A cube with side length 4 units is built from unit cubes. How many cubes fit inside?
64 cubic units (since 4×4×4 = 64)
A prism has a base of 3 cm by 6 cm and a volume of 54 cm³. What is its height?
Volume ÷ (base area) = 54 ÷ (3×6 = 18) = 3 cm
A prism’s volume is 100 cubic cm. The base is 10 × 2. What is the missing height?
100 ÷ (10×2 = 20) = 5 cm
A prism has a volume of 36. Which sets of dimensions could it have? (Choose two: 3×3×4, 2×6×3, 6×6×1)
Correct sets: 3×3×4 = 36, 2×6×3 = 36.
A cereal box is 10 in tall with a base of 3 in × 2 in. What is its volume?
10 × 3 × 2 = 60 in³
Which shapes below could have a volume of 30 cubic units: 2×3×5, 6×2×2, or 3×3×3?
Correct shapes: 2×3×5 and 3×3×3 (both = 30 & 27 → actually only 2×3×5 = 30, so the answer is just 2×3×5)
A cube has a volume of 64 cubic cm. What is its side length?
Cube side length = ∛64 = 4 cm
A prism has a height of 9 cm, width 2 cm, and unknown length. If the volume is 108 cm³, what is the length?
108 ÷ (9×2 = 18) = 6 cm
Write an equation you would solve to find the height of a prism with volume 72 and base 4 × 6.
Equation: 4 × 6 × h = 72 → h = 3
A swimming pool is 12 m long, 4 m wide, and 2 m deep. How many cubic meters of water can it hold?
12 × 4 × 2 = 96 m³
A toy box is filled with 27 unit cubes. What is the correct way to describe its volume: square units or cubic units?
Volume is measured in cubic units
A box has a base area of 20 square units and a height of 7 units. What is its volume?
20 × 7 = 140 cubic units
A cube has a volume of 125 cubic inches. What is its edge length?
∛125 = 5 inches
A prism has a base of 10 × 3 and height h. Write an expression for its volume.
Expression: 10 × 3 × h = 30h
A shipping container has a base of 5 m × 6 m and a volume of 150 m³. What is the container’s height?
150 ÷ (5×6 = 30) = 5 m