Volume of Right Prisms
Match Prism to Cross-Section Formula
Draw a line to match each prism to the formula for its cross-section area.
V = Cross-Section Area × Length
Circle the correct volume.
Cross-section = 12 cm², length = 8 cm
Cross-section = 25 m², length = 6 m
Cross-section = 30 cm², length = 5 cm
Triangular Prism Volume
Find cross-section area (triangle) then multiply by length.
Base 6 cm, height 4 cm, length 10 cm
Base 8 m, height 3 m, length 7 m
Base 5 cm, height 5 cm, length 8 cm
Find the Missing Dimension
Rearrange V = Ah to find the unknown.
V = 240 cm³, A = 30 cm². Length =
V = 180 m³, length = 12 m. Cross-section area =
V = 120 cm³, l = 5 cm, w = 4 cm. Height =
Best Unit for Volume
Match each context to the most appropriate unit.
Volume in Context
Show all working.
A pool is 25 m long, 10 m wide, depth 1.8 m. Volume in m³? Capacity in litres? (1 m³ = 1000 L)
A triangular prism tent has cross-section: base 2.4 m, height 1.8 m. Length 3 m. Volume of air inside?
Volume of a Cylinder
A cylinder is a circular prism. Use V = πr²h. Use π ≈ 3.14.
r = 5 cm, h = 10 cm
r = 3 m, h = 7 m
Diameter = 8 cm, h = 6 cm
Surface Area of a Rectangular Prism
Surface area = 2(lw + lh + wh). Find the total surface area.
l = 5 cm, w = 3 cm, h = 4 cm
l = 10 m, w = 2 m, h = 3 m
Cube, side 6 cm. Surface area =
Compare Volumes of Different Prisms
Each prism has cross-section area 12 cm². Rank by volume (cross-section × length).
Volume Word Problems with Rates
Show all working and include units.
A cylindrical water tank has radius 2 m and height 3 m. Water fills it at a rate of 0.5 m³ per minute. How long does it take to fill? (Use π ≈ 3.14, round to the nearest minute.)
A rectangular fish tank is 60 cm long, 30 cm wide and 40 cm tall. It is currently half full. How many litres of water must be added to fill it? (1 litre = 1000 cm³)
Volume Formula Match
Draw a line to match each solid to its volume formula.
Volume at Home
Explore volume and capacity in everyday objects.
- 1Measure a cardboard box (cereal box, shoe box). Calculate its volume in cm³ and convert to litres. Compare to the volume stated on the packaging.
- 2Find two cylindrical containers (e.g. tin cans). Measure the radius and height. Calculate the volume of each. Which holds more?
- 3Fill a container with water and pour it into a measuring jug. Compare the measured volume (in mL) to the calculated volume. How close is your calculation?
Volume of Rectangular Prism
Use V = lwh.
l = 6 cm, w = 4 cm, h = 3 cm:
l = 10 m, w = 5 m, h = 2 m:
Cube with side 4 cm:
l = 2.5 m, w = 1.5 m, h = 0.8 m:
Finding a Missing Dimension from Volume
Rearrange V = Ah to find the unknown. Show all working.
A rectangular prism has volume 120 cm³, length 5 cm, width 4 cm. Find the height.
A triangular prism has volume 90 m³ and length 9 m. The triangle base is 5 m. Find the perpendicular height of the triangle.
A cylinder has volume 628 cm³ and radius 5 cm. Find its height. (Use π ≈ 3.14.)
Surface Area of a Rectangular Prism
Use SA = 2(lw + lh + wh).
l = 5 cm, w = 3 cm, h = 4 cm:
l = 10 m, w = 2 m, h = 3 m:
Cube with side 6 cm:
l = 4 m, w = 4 m, h = 2 m:
Surface Area of a Triangular Prism
A triangular prism has 5 faces: 2 triangular ends and 3 rectangular sides. Find the total surface area.
Triangular prism: triangle has base 6 cm and height 4 cm. Prism length = 10 cm. The three rectangle widths are 6 cm, 5 cm, and 5 cm (an isosceles triangle). Find the total surface area.
Why is knowing the surface area important for a manufacturer making tin cans? Write two sentences.
Volume in Context — Water and Tanks
Show all working. Use π ≈ 3.14.
A pool is 25 m long, 10 m wide, 1.8 m deep. Volume in m³? Capacity in litres? If the pool empties at 3 m³/min, how long to empty?
A cylindrical tank has diameter 2.4 m and height 3 m. Calculate its capacity in litres. If water is pumped in at 50 litres per minute, how long to fill it?
Best Unit for Volume
Match each context to the most appropriate unit.
Design Challenge — Box with Minimum Surface Area
Investigate the relationship between volume and surface area.
Design a box (rectangular prism) with volume exactly 1000 cm³. Try three different sets of dimensions. Calculate the surface area for each. Which uses the least material?
Based on your investigation, what shape minimises surface area for a fixed volume? How does this relate to the shape of eggs and bubbles?
Comparing Volumes
Without full calculation, decide which has greater volume.
Cylinder r=3, h=4 vs rectangular prism 6×4×4:
Doubling the height of a cylinder vs doubling the radius:
Cube with side 5 cm vs sphere with radius 3 cm (V = 4/3 πr³ ≈ 113 cm³):
Scale Factor and Volume
Explore how scale factors affect volume.
A model car is built at scale 1:20. The real car engine has volume 2000 cm³. What is the volume of the model engine? Show your reasoning using the scale factor cubed.
If a cube has side 4 cm (volume 64 cm³) and you double all its dimensions, what is the new volume? By what factor did the volume change?
Volume Investigation — Cylinders vs Boxes
Compare volumes for given surface areas.
A manufacturer has 600 cm² of material to make a can. Option A: cylinder with radius 5 cm. Find the height and volume. Option B: cube with maximum side length. Compare which holds more. Show all working.
Why might manufacturers choose a cylindrical can over a rectangular box of the same volume? Write at least two mathematical and practical reasons.
Rectangular Prism Volume — Set A
Calculate the volume of each rectangular prism.
l = 8 cm, w = 5 cm, h = 3 cm
l = 12 m, w = 4 m, h = 2.5 m
l = 0.6 m, w = 0.4 m, h = 0.3 m. Give answer in cm³.
Triangular Prism Volume — Set A
Calculate the volume of each triangular prism.
Triangle: base 6 cm, height 4 cm. Prism length 10 cm.
Triangle: base 8 m, height 3 m. Prism length 5 m.
A triangular prism has cross-section area 15 cm² and length 12 cm. Find its volume.
Identify the Cross-Section
Circle the shape that describes the cross-section of each prism.
A triangular prism
A cylinder
A rectangular prism (cuboid)
A trapezoidal prism
Cylinder Volume — Set A
Calculate the volume of each cylinder. Use π ≈ 3.14.
r = 5 cm, h = 10 cm
Diameter = 8 m, h = 3 m
r = 2.5 cm, h = 12 cm. Give answer to nearest cm³.
Capacity from Volume
Find the volume then convert to litres.
A rectangular fish tank: 60 cm × 30 cm × 40 cm. Find volume in cm³ then convert to litres.
A cylindrical bucket: radius 15 cm, height 25 cm. Find volume in cm³ then convert to litres. (π ≈ 3.14)
A swimming pool (rectangular): 10 m × 5 m × 1.8 m deep. Volume in m³, then convert to kilolitres (1 m³ = 1 kL).
Trapezoidal Prism Volume
Calculate the volume of each trapezoidal prism.
Trapezium: parallel sides 4 cm and 8 cm, height 5 cm. Prism length 10 cm.
Trapezium: parallel sides 3 m and 7 m, height 4 m. Prism length 6 m.
Finding Missing Dimensions
Rearrange the volume formula to find the unknown dimension.
A rectangular prism has V = 360 cm³, l = 12 cm, w = 5 cm. Find h.
A cylinder has V = 502.4 cm³ and h = 8 cm. Find r. (π ≈ 3.14)
A triangular prism has V = 180 cm³. The cross-section is a right triangle with base 6 cm and height 5 cm. Find the prism's length.
Match the Volume Formula
Match each shape to its volume formula.
Real-World Volume: Storage
Solve each practical problem. Show full working.
A shipping container is 12 m long, 2.4 m wide, and 2.6 m tall. Find its volume. If boxes are 0.3 m × 0.3 m × 0.3 m, how many boxes fit in one layer on the floor?
A grain silo is a cylinder with radius 3 m and height 8 m. Find the volume. If grain weighs 0.8 kg per litre, how many kg of grain can the silo hold?
Swimming Pool Problem
Solve this multi-step volume problem.
A swimming pool has a trapezoidal cross-section: deep end 2.5 m, shallow end 1.2 m, length 25 m, width 10 m. (a) Find the cross-section area. (b) Find the pool's volume. (c) Convert to kilolitres. (d) At $0.003 per litre for water, what does it cost to fill?
Cylinder Volume — Set B
Solve each cylinder problem. Use π ≈ 3.14.
A hot water cylinder has diameter 0.5 m and height 1.8 m. Find its volume in m³ and convert to litres.
A cylindrical drinking glass has radius 4 cm and height 12 cm. How many mL does it hold when full?
Three identical cylinders each have radius 3 cm and height 10 cm. What is their combined volume?
Sort by Volume (Smallest to Largest)
Estimate or calculate, then sort from smallest to largest volume.
Volume Unit Conversions
Convert each volume to the specified unit. Show working.
Convert 2 m³ to cm³.
Convert 500 000 cm³ to m³.
A tank holds 1.5 m³. Express this in: (a) litres (b) mL.
Error Analysis — Volume Mistakes
Find the error in each student solution and provide the correct answer.
Student: 'Cylinder with diameter 6 cm, h = 10 cm. V = π × 6² × 10 = 1130.4 cm³.' What is the error? Find the correct volume.
Student: 'Triangular prism: base 8 cm, height 6 cm, length 5 cm. V = 8 × 6 × 5 = 240 cm³.' What is the error? Find the correct volume.
Composite Solid Volume
Find the total volume of each composite solid.
A shed has a rectangular prism base (6 m × 4 m × 2.5 m) and a triangular prism roof (triangle: base 4 m, height 1.5 m; length 6 m). Find the total volume.
A block of wood is a 10 cm cube with a cylindrical hole drilled through it (r = 2 cm, same height as cube). Find the volume of wood remaining. (π ≈ 3.14)
Volume Formula Check
Circle the correct formula or calculation for each scenario.
Volume of a prism with cross-section area A and length L:
A cylinder with r = 4 cm and h = 7 cm. First step:
To find the height of a rectangular prism given V, l, w:
Prism Investigation: Same Volume, Different Shapes
Explore how different prisms can have the same volume.
A rectangular prism has V = 120 cm³. List four different sets of integer dimensions (l, w, h) that give this volume.
A triangular prism has V = 120 cm³. If the prism length is 10 cm, what must the cross-section area be? List two different triangles (base, height) that give this area.
Design Problem: Packaging
Use volume to solve a practical design problem.
A company needs to pack 1 litre (1000 cm³) of juice. Design A: cylinder with radius 5 cm. Design B: rectangular prism with square base side 8 cm. Find the height needed for each container. Which do you think is better? Explain with mathematics.
Problem Solving: Concrete and Construction
Solve each construction-related volume problem.
A concrete driveway is 12 m long, 3 m wide, and 0.1 m thick. Find the volume of concrete needed in m³. Concrete costs $250 per m³. Find the total cost.
A cylindrical column is 0.3 m in diameter and 4 m tall. Twelve identical columns are needed. Find the total volume of concrete for all columns. (π ≈ 3.14)
Extended Investigation: Volume Scaling
Investigate how volume changes with scale.
A rectangular prism has l = 3 cm, w = 2 cm, h = 4 cm. Complete the table: scale factor 1, 2, 3, 4 — calculate new dimensions and volume for each. What pattern do you notice?
A model building is built at scale 1:100. The model has volume 500 cm³. What is the actual building's volume in m³?
Reflection: Volume of Right Prisms
Consolidate your learning about volume.
In your own words, explain why the formula V = Ah works for all right prisms. Why is the cross-section area so important?
Give one real-world example where calculating volume is important. Describe what would happen if the volume calculation was wrong.
What is one thing you found difficult about this topic, and what strategy did you use to overcome it?