Problem 1: Counting unit cubes
Each layer has \(3 \times 2 = 6\) cubes, and there are 2 layers: \(6 \times 2 = 12\).
Answer: 12 cubic units.
Problem 2: Counting layers
One layer has \(4 \times 3 = 12\) cubes. There are 2 layers. Volume: \(12 \times 2 = 24\).
Answer: 12 cubes per layer, 2 layers, 24 cubic units.
Problem 3: Volume in centimeters
\(V = l \times w \times h = 5 \times 4 \times 3 = 60\).
Answer: \(60\text{ cm}^{3}\).
Problem 4: Volume in feet
\(V = 8 \times 2 \times 6 = 16 \times 6 = 96\).
Answer: \(96\text{ ft}^{3}\).
Problem 5: Using base area
\(V = B \times h = 20 \times 7 = 140\).
Answer: \(140\text{ in}^{3}\).
Problem 6: Volume of a cube
All three edges are 6 in: \(V = 6 \times 6 \times 6 = 36 \times 6 = 216\).
Answer: \(216\text{ in}^{3}\).
Problem 7: Base first, then height
\(B = 7 \times 5 = 35\) square meters. \(V = 35 \times 4 = 140\).
Answer: B = \(35\text{ m}^{2}\); V = \(140\text{ m}^{3}\).
Problem 8: Missing height
\(6 \times 5 \times h = 90\), so \(30 \times h = 90\). Since \(30 \times 3 = 90\), \(h = 3\).
Answer: \(3\text{ cm}\).
Problem 9: Height from base area
\(36 \times h = 144\), so \(h = 144 : 36 = 4\).
Answer: \(4\text{ ft}\).
Problem 10: Missing length
\(l \times 4 \times 5 = 120\), so \(l \times 20 = 120\) and \(l = 6\).
Answer: \(6\text{ in}\).
Problem 11: Which holds more
A: \(6 \times 4 \times 5 = 120\). B: \(7 \times 3 \times 6 = 126\). Difference: \(126 – 120 = 6\).
Answer: Prism B is greater by \(6\text{ in}^{3}\).
Problem 12: Cubes in layers
\(15 \times 4 = 60\).
Answer: 60 cubic units.
Problem 13: Choose the unit
\(10 \times 6 \times 4 = 240\). Volume uses cubic units.
Answer: \(240\text{ in}^{3}\).
Problem 14: Composite solid, two parts
Blue: \(4 \times 3 \times 3 = 36\). Orange: \(3 \times 3 \times 1 = 9\). Total: \(36 + 9 = 45\).
Answer: \(45\text{ ft}^{3}\).
Problem 15: Staircase solid
Step 1: \(2 \times 4 \times 1 = 8\). Step 2: \(2 \times 4 \times 2 = 16\). Step 3: \(2 \times 4 \times 3 = 24\).
Total: \(8 + 16 + 24 = 48\).
Answer: \(48\text{ ft}^{3}\).
Problem 16: Packing a box
Each cube is \(1\text{ in}^{3}\). \(12 \times 9 \times 6 = 108 \times 6 = 648\).
Answer: 648 cubes.
Problem 17: Check a prism
\(5 \times 3 \times 2 = 15 \times 2 = 30\).
Answer: Yes; the product of the three edges is 30 cubic units.
Problem 18: Sandbox
Volume: \(8 \times 5 \times 1 = 40\) cubic feet. Bags: \(40 : 2 = 20\).
Answer: 20 bags.
Problem 19: Fish tank
Water: \(24 \times 12 \times 8 = 288 \times 8 = 2{,}304\). Full tank: \(288 \times 10 = 2{,}880\). More: \(2{,}880 – 2{,}304 = 576\).
Answer: \(2{,}304\text{ in}^{3}\) of water; \(576\text{ in}^{3}\) more.
Problem 20: Storage boxes
First box: \(6 \times 4 \times 3 = 72\). Second box: \(4 \times 4 \times 2 = 32\). Total: \(72 + 32 = 104\).
Answer: \(104\text{ ft}^{3}\).
Problem 21: Filling a pool
Volume: \(15 \times 10 \times 4 = 600\) cubic feet. Time: \(600 : 50 = 12\).
Answer: 12 hours.
Problem 22: Moving truck
Cargo space: \(10 \times 8 \times 6 = 480\). One box: \(2 \times 2 \times 2 = 8\). \(480 : 8 = 60\).
Answer: 60 boxes.
See every chapter on the Grade 5 math page.