← Back to the Volume Of Rectangular Prisms worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Each solution shows the cube count or the formula, the substitution and a check. If your volume differs, look first for a unit mismatch or for edges that were added instead of multiplied.
Standards: 6.G.A.2 · Level: Grade 6
Problem 1 Counting unit cubes
One layer holds 4 × 3 = 12 cubes. There are 2 layers, so 12 × 2 = 24.
24 cubic units
Problem 2 Volume of a box
V = 9 × 4 × 5 = 36 × 5 = 180.
180 cubic inches
Problem 3 Volume of a cube
V = 8 × 8 × 8 = 512.
512 cubic centimeters
Problem 4 Volume from the base area
V = Bh = 24 × 7 = 168.
168 cubic feet
Problem 5 A small metric box
V = 10 × 6 × 4 = 60 × 4 = 240.
240 cubic centimeters
Problem 6 Packing with half-foot cubes
- The prism holds 2 ft ÷ ½ ft = 4 cubes along the length, 3 along the width and 2 along the height: 4 × 3 × 2 = 24 cubes.
- One cube: ½ × ½ × ½ = 18 cubic foot.
- 24 × 18 = 3. Check: 2 × 1½ × 1 = 3.
(a) 24 cubes; (b) 18 ft³; (c) 3 cubic feet
Problem 7 A prism with fractional edges
V = 52 × 2 × 32 = 5 × 32 = 152 = 712.
7½ cubic inches
Problem 8 Missing height
180 = 9 × 5 × h = 45h, so h = 180 ÷ 45 = 4. Check: 9 × 5 × 4 = 180.
4 feet
Problem 9 Volume with decimals
V = Bh = 3.5 × 4 = 14.
14 cubic meters
Problem 10 Fish tank
V = 24 × 12 × 15 = 288 × 15 = 4,320.
4,320 cubic inches
Problem 11 Cube with a fraction edge
V = 34 × 34 × 34 = 2764.
2764 cubic inch
Problem 12 Packing with quarter-foot cubes
- Along the length 54 ÷ 14 = 5 cubes, along the width 12 ÷ 14 = 2 cubes, along the height 34 ÷ 14 = 3 cubes: 5 × 2 × 3 = 30 cubes.
- One cube is 14 × 14 × 14 = 164 cubic foot, so the volume is 30 × 164 = 3064 = 1532. Check: 54 × 12 × 34 = 1532.
(a) 30 cubes; (b) 1532 cubic foot
Problem 13 Missing width
96 = 8 × w × 3 = 24w, so w = 96 ÷ 24 = 4.
4 centimeters
Problem 14 Comparing two boxes
Box A: 14 × 6 × 5 = 84 × 5 = 420. Box B: 10 × 8 × 5.5 = 80 × 5.5 = 440. The difference is 440 − 420 = 20.
Box B is greater by 20 cubic inches
Problem 15 Sand for a sandbox
- 8 × 5.5 × 0.75 = 44 × 0.75 = 33 cubic feet.
- 33 ÷ 2.5 = 13.2, so 13 bags are not enough: 14 bags.
- 14 × 4.50 = 63.
(a) 33 ft³; (b) 14 bags; (c) $63
Problem 16 Water in an aquarium
- 20 × 10 × 12 = 2,400.
- The water depth is 34 × 12 = 9 inches, so 20 × 10 × 9 = 1,800.
- 2,400 − 1,800 = 600.
(a) 2,400 in³; (b) 1,800 in³; (c) 600 in³
Problem 17 Concrete slab
- 12 × 9 × 13 = 108 × 13 = 36 cubic feet.
- 36 × 6.25 = 225.
(a) 36 ft³; (b) $225
Problem 18 Filling a gift box
- 7.5 ÷ 1.5 = 5, 4.5 ÷ 1.5 = 3 and 3 ÷ 1.5 = 2, so 5 × 3 × 2 = 30 cubes.
- 7.5 × 4.5 × 3 = 33.75 × 3 = 101.25 cubic inches.
- One cube is 1.5 × 1.5 × 1.5 = 3.375, and 101.25 ÷ 3.375 = 30, which matches part (a).
(a) 30 cubes; (b) 101.25 in³; (c) 3.375 in³ per cube
Problem 19 Filling a pool
- 20 × 12 × 5 = 1,200 cubic feet.
- The depth is 5 − 0.5 = 4.5 feet, so 20 × 12 × 4.5 = 240 × 4.5 = 1,080.
- 1,080 ÷ 30 = 36.
(a) 1,200 ft³; (b) 1,080 ft³; (c) 36 minutes
Problem 20 Changing the height
270 = 7.5 × 4 × h = 30h, so h = 9. The second prism has height 4.5 inches: 7.5 × 4 × 4.5 = 135. Half the height gives half the volume: 270 ÷ 2 = 135.
Height 9 inches; second volume 135 cubic inches