Mathematics • Year 8 • Unit 3 • Lesson 10

Volume of Prisms

Build fluency with V = A_base × h for any prism — and the capacity conversions 1 cm³ = 1 mL, 1000 cm³ = 1 L, 1 m³ = 1000 L.

Build · I Do / We Do / You Do

1. I do — fully worked example

The big idea: find the cross-section area first, then multiply by the prism's length.

Problem. A triangular prism has a triangle cross-section with base 8 cm, perpendicular height 5 cm. The prism length is 12 cm. Find its volume.

Step 1 — Identify the cross-section.

Cross-section = the triangle (the shape that stays constant as you slice along the prism).

Reason: the cross-section is NOT a rectangular side of the prism. It's the shape that is identical at both ends.

Step 2 — Find the cross-section area.

A_triangle = ½ × b × h_△ = ½ × 8 × 5 = 20 cm²

Step 3 — Multiply by the prism length.

V = A_base × l = 20 × 12 = 240 cm³

Reason: V = A_base × h applies to EVERY prism — rectangular, triangular, trapezoidal, L-shaped.

Answer: V = 240 cm³ (always cubic units).

Stuck? Revisit lesson § Card 4 — "Spot the Trap": don't use the prism length as the triangle's height.

2. We do — fill in the missing steps

A rectangular prism with l = 7 cm, w = 5 cm, h = 4 cm. Fill in each blank. 4 marks

Step 1 — Identify the cross-section: the cross-section is a ______________ with dimensions ______ × ______.

Step 2 — Find the cross-section area:

A_base = ______ × ______ = ______ cm²

Step 3 — Multiply by the prism height:

V = ______ × ______ = ______ cm³

Step 4 — Convert to mL (since 1 cm³ = 1 mL):

Capacity = ______ mL

Stuck? Revisit lesson § Card 5 — for a rectangular prism, V = lwh.

3. You do — independent practice

Show all working. Foundation: rectangular prisms. Standard: triangular and composite. Extension: capacity conversions.

Foundation — rectangular prisms

3.1 Find V of a cube with side 6 cm. 1 mark

3.2 Box: l = 4 cm, w = 5 cm, h = 6 cm. Find V. 1 mark

3.3 Box: l = 12 cm, w = 8 cm, h = 5 cm. Find V. 1 mark

3.4 Box: l = 2 m, w = 1.5 m, h = 0.8 m. Find V (m³). 1 mark

Standard — triangular and L-shaped prisms

3.5 Triangular prism: triangle base 10 cm, triangle height 6 cm, prism length 8 cm. Find V. 2 marks

3.6 An L-shaped prism. Cross-section is split into two rectangles: R₁ is 4 cm × 8 cm, R₂ is 3 cm × 5 cm. Prism length is 10 cm. Find V. (Hint: A_base = A_R1 + A_R2, then V = A × l.) 2 marks

Extension — convert to litres / millilitres

3.7 A juice carton is a rectangular prism: 20 cm × 10 cm × 5 cm. Find V in cm³, then convert to mL and L. 2 marks

3.8 A swimming pool is 8 m long, 4 m wide, and 1.5 m deep. Find V in m³, then convert to litres. (Hint: 1 m³ = 1 000 L.) 2 marks

Stuck on 3.7 / 3.8? Conversions: cm³ → mL (same number); cm³ → L (÷ 1000); m³ → L (× 1000).

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do (7 × 5 × 4 box)

Step 1: cross-section is a rectangle, 7 × 5.
Step 2: A_base = 7 × 5 = 35 cm².
Step 3: V = 35 × 4 = 140 cm³.
Step 4: Capacity = 140 mL.

3.1 — Cube, side 6

V = 6 × 6 × 6 = 216 cm³.

3.2 — Box 4 × 5 × 6

V = 4 × 5 × 6 = 120 cm³.

3.3 — Box 12 × 8 × 5

V = 12 × 8 × 5 = 480 cm³.

3.4 — Box 2 × 1.5 × 0.8 m

V = 2 × 1.5 × 0.8 = 2.4 m³.

3.5 — Triangular prism (b = 10, h_△ = 6, l = 8)

A_triangle = ½ × 10 × 6 = 30 cm². V = 30 × 8 = 240 cm³.

3.6 — L-shaped prism

A_R1 = 4 × 8 = 32 cm². A_R2 = 3 × 5 = 15 cm². A_base = 32 + 15 = 47 cm².
V = 47 × 10 = 470 cm³.

3.7 — Juice carton 20 × 10 × 5

V = 20 × 10 × 5 = 1000 cm³ = 1000 mL = 1 L.

3.8 — Pool 8 × 4 × 1.5 m

V = 8 × 4 × 1.5 = 48 m³ = 48 000 L.