Volume of Rectangular & Triangular Prisms
Match Prism to Formula
Draw a line from each prism type to its volume formula.
Volume of Rectangular Prisms
Use V = l × w × h. Circle the correct volume.
l = 4 cm, w = 3 cm, h = 5 cm
l = 6 m, w = 6 m, h = 6 m
l = 10 cm, w = 4 cm, h = 2 cm
Volume of Triangular Prisms
Use V = ½ × b × h × length. Circle the correct volume.
b = 4 cm, h = 3 cm, length = 10 cm
b = 6 m, h = 4 m, length = 5 m
b = 8 cm, h = 6 cm, length = 7 cm
Volume Units
Sort each measurement into the correct unit category.
Volume of a Cube
Use V = s³ where s is the side length.
Cube with side 3 cm
Cube with side 5 m
Cube with side 10 cm
Cube with side 0.5 m
Volume Word Problems — Foundational
Solve each problem and show your working.
A box is 8 cm long, 5 cm wide, and 4 cm tall. What is its volume?
A triangular wedge of cheese has a triangular face with base 6 cm and height 4 cm. The wedge is 8 cm long. What is its volume?
Capacity Conversions — L and cm³
Use 1 L = 1000 cm³.
3500 cm³ = ? L
600 L = ? cm³
250 mL = ? cm³
Order by Volume
Calculate each volume, then sort from smallest to largest.
Fish Tank Volume
Solve this real-world problem.
A fish tank is 60 cm long, 30 cm wide, and 40 cm high. What is its volume in cm³? How many litres of water does it hold? (1 L = 1000 cm³)
Drawing Prisms
Sketch and label the following prisms.
Sketch a rectangular prism with dimensions 6 cm × 4 cm × 3 cm. Label each dimension and calculate the volume.
Sketch a triangular prism with a triangular face of base 5 cm and height 4 cm, and a length of 10 cm. Calculate the volume.
Match Volume to Real Object
Sort each object under the most likely volume.
Missing Dimension Problems
Rearrange the volume formula to find the unknown dimension. Show all steps.
A rectangular prism has volume 120 cm³, length 6 cm, and width 4 cm. What is the height?
A rectangular prism has volume 240 m³ and a base area of 30 m². What is the height?
A triangular prism has volume 90 cm³, base 6 cm, and length 10 cm. What is the height of the triangular face?
Comparing Volumes
Compare the volumes of these prisms.
Box A: 8 cm × 5 cm × 3 cm. Box B: triangular prism with b=8cm, h=5cm, l=6cm. Which has the larger volume? By how much?
Cube A has side 4 cm. Cube B has side 8 cm. How many times larger is Cube B's volume than Cube A's volume?
Volume Story Problems
Solve each story problem. Show your working.
A triangular prism-shaped tent has a triangular cross-section with base 3 m and height 2 m. The tent is 4 m long. What is the volume of space inside the tent?
A cardboard box is 50 cm long, 30 cm wide, and 20 cm high. How many litres of sand could it hold? (1 L = 1000 cm³)
Volume Scaling
Circle the correct answer about scaled volumes.
A rectangular prism has volume 24 cm³. All dimensions are doubled. New volume?
A cube has volume 27 cm³. Its side is tripled. New volume?
A prism has volume 100 m³. Its length is halved. New volume?
Building Project — Volume
Use volume calculations to plan a construction project.
A garden bed is rectangular, 4 m long and 1.2 m wide. Compost must be filled to a depth of 30 cm (0.3 m). What volume of compost is needed in m³? How many litres is that?
Design a Box — Volume Constraint
Design a rectangular box to meet given specifications.
Design a rectangular box with volume exactly 120 cm³. Find at least 4 different sets of integer dimensions (l, w, h) that work. Which design has the smallest total surface area?
Volume Investigation — Cereal Box
Conduct an investigation using a real box.
Find a cereal box (or other rectangular box). Measure its length, width, and height. Calculate its volume in cm³ and convert to litres. Compare with the volume printed on the box (if any). Explain any difference.
Volume Sequence — Growing Boxes
A rectangular box has l=1cm and w=1cm. Its height increases by 1 cm each step. Fill in the missing volumes.
Volume of an L-Shaped Prism
Find the volume of each composite prism by splitting into rectangular prisms.
An L-shaped prism (when viewed from the end) has two rectangular sections: 8×4 cm and 3×4 cm, joined. The prism is 10 cm long. What is the total volume?
A stepped prism has cross-section made of two rectangles: 6×2 cm (lower) and 3×4 cm (upper), joined. The prism is 5 cm long. What is the volume?
Swimming Pool Design
Solve this multi-step volume problem.
A swimming pool is 25 m long, 10 m wide, and 1.5 m deep. How many litres of water does it hold? If a hose fills at 50 litres per minute, how long will it take to fill the pool? Give your answer in hours and minutes.
Volume with Holes
Find the volume of each solid that has a portion removed.
A block of wood is 10 cm × 8 cm × 6 cm. A rectangular hole 2 cm × 2 cm × 6 cm is drilled through it. What is the remaining volume?
A triangular prism of concrete (b=6m, h=4m, l=20m) has a rectangular duct (0.5m × 0.5m × 20m) running through it. What is the remaining volume of concrete?
Volume Sequence — Scaling Cubes
Fill in the volume of each cube as the side length increases by 1 cm.
Concrete Calculations
Solve these construction volume problems.
A driveway is 8 m long, 3 m wide, and 10 cm (0.1 m) thick. What volume of concrete is needed in m³? Concrete costs $180 per m³. What is the total cost?
A triangular prism-shaped ramp has a cross-section with base 2 m and height 0.5 m. The ramp is 3 m long. How many kg of gravel fills it if gravel has density 1800 kg/m³?
Compare Two Prisms — Same Volume Different Shape
Investigate prisms with equal volumes but different shapes.
A rectangular prism 12 × 5 × 4 cm and a triangular prism with b=10cm, h=8cm, l=6cm. Do they have the same volume? Show calculations.
Design a triangular prism with the same volume as a 10 × 4 × 6 cm rectangular box. Give the dimensions of the triangular cross-section and the length.
Rainwater Tank Planning
Apply volume knowledge to plan a rainwater tank.
A family wants a rectangular rainwater tank with volume 2000 L (2 m³). Suggest suitable dimensions (l, w, h in metres) for the tank. Justify your choice in terms of practicality — not too tall, fits in the yard.
If the roof area is 150 m² and the average monthly rainfall is 50 mm (0.05 m), how many litres of rain can be collected each month? (Volume = roof area × rainfall depth)
Irregular Volume by Displacement
Use Archimedes' displacement method to find the volume of an irregular object.
A stone is placed in a rectangular container 10 cm × 8 cm. The water level rises by 1.5 cm. What is the volume of the stone?
Describe how you would use displacement to find the volume of a handful of marbles. What measurement would you take and how would you calculate the volume?
Volume of Composite 3D Shapes
Find the volume of each composite 3D shape.
A shape is made of a rectangular prism (8 × 5 × 4 cm) with a triangular prism on top (b=8cm, h=3cm, l=5cm). What is the total volume?
A rectangular block 20×15×10 cm has a cylinder-shaped hole 4 cm in diameter and 10 cm deep (use π ≈ 3.14, V_cylinder = πr²h). Find the remaining volume.
Volume of a Pyramid vs Prism
Investigate the relationship between a pyramid and a prism with the same base and height.
A rectangular pyramid has base 6 cm × 4 cm and height 5 cm. Use V = (1/3) × base area × height to find its volume.
Compare the pyramid's volume with a rectangular prism of the same base and height. What fraction is the pyramid of the prism?
Optimisation — Minimum Surface Area for Fixed Volume
Investigate the relationship between surface area and volume for rectangular prisms.
Find 5 rectangular prisms with volume 64 cm³ (integer dimensions). Calculate the surface area of each. Which shape has the minimum surface area?
What does your investigation suggest about the most efficient shape for packaging? How does this relate to the cube shape commonly used in gift boxes?
Rates and Volume — Engineering Context
Apply volume and rate calculations to an engineering problem.
A hydroelectric dam releases water through a rectangular channel 3 m wide and 2 m deep at a speed of 4 m/s. How many m³ of water pass through per second? Per minute? Per hour?
If this water drives a turbine at 80% efficiency and 1 m³/s generates 100 kW of power, how many kW does this dam generate? How many homes (each using 8 kW on average) could it power?
Volume Research Task
Research and apply volume calculations to a real-world structure.
Research the dimensions of the Great Pyramid of Giza (base approx 230 m × 230 m, height 138 m). Calculate its approximate volume using the pyramid formula V = (1/3)× base area × height. Compare it to the volume of 1 million cubic metres.
Explain why the pyramid shape is structurally efficient — why do ancient builders use it rather than a rectangular prism of the same base area?
Critical Thinking — Volume and Sustainability
Apply volume knowledge to a sustainability context.
A household uses 150 litres of water per person per day. A family of 4 wants to collect enough rainwater to cover 30 days of use. Their roof area is 200 m². What average monthly rainfall (in mm) is needed to fill the required volume? (V = area × depth)
Volume Investigation at Home
Explore volume using containers and objects at home.
- 1Find a rectangular box (cereal box, shoebox). Measure all dimensions and calculate its volume. Convert to litres. Compare with any volume printed on the packaging.
- 2Fill a 1-litre bottle with water and pour it into a rectangular container. Measure the water level height. Does your calculated volume match?
- 3Use displacement: fill a container with water, submerge an object, and measure how much the water level rises. Use this to calculate the object's volume.
- 4Challenge: find a triangular prism-shaped object at home (a Toblerone box, a tent, a wedge doorstop). Measure its dimensions and calculate its volume.