Year 8 Mathematics | Victorian Curriculum 2.0
Volume of right prisms
Topic 09 | Measurement & Space | Practice

What you will learn

1. The key idea: base area × length

Volume of a right prism
V=Abase×L,V = A_{\text{base}} \times L,

where AbaseA_{\text{base}} is the area of the prism’s cross-section (a constant shape along its length), and LL is the length (the distance between the two matching ends).

rectangulartriangulartrapezoidal
Three right prisms. The shaded end is the cross-section (the base). Volume = cross-section area × length.
Worked example 1 Rectangular prism

A box is 88 cm by 55 cm by 44 cm.

V=8×5×4=160 cm3.V = 8 \times 5 \times 4 = 160 \text{ cm}^3.
Worked example 2 Triangular prism

A tent has a triangular cross-section of base 2.42.4 m and height 1.81.8 m, and is 33 m long.

  1. Triangle area: 12×2.4×1.8=2.16\tfrac{1}{2} \times 2.4 \times 1.8 = 2.16 m2^2.
  2. Volume: 2.16×3=6.482.16 \times 3 = 6.48 m3^3.
Worked example 3 Trapezoidal prism

A channel has a trapezoidal cross-section: parallel sides 1.51.5 m and 2.52.5 m, height 0.80.8 m. It is 2020 m long.

  1. Trapezium area: 12(1.5+2.5)×0.8=1.6\tfrac{1}{2}(1.5 + 2.5) \times 0.8 = 1.6 m2^2.
  2. Volume: 1.6×20=321.6 \times 20 = 32 m3^3.

2. Volume ↔ capacity

Conversions

Volume units
1 cm3=1000 mm3,1 m3=1 000 000 cm3.1 \text{ cm}^3 = 1000 \text{ mm}^3, \qquad 1 \text{ m}^3 = 1\,000\,000 \text{ cm}^3.
Capacity units
1 L=1000 mL,1 kL=1000 L.1 \text{ L} = 1000 \text{ mL}, \qquad 1 \text{ kL} = 1000 \text{ L}.
Linking volume and capacity
1 cm3=1 mL,1 m3=1000 L=1 kL.1 \text{ cm}^3 = 1 \text{ mL}, \qquad 1 \text{ m}^3 = 1000 \text{ L} = 1 \text{ kL}.

3. Rates and time to fill

If a volume VV is delivered at a constant rate rr, the time to fill is t=Vrt = \dfrac{V}{r}.

Worked example 4 Filling a tank

A rectangular tank is 22 m by 1.51.5 m by 1.21.2 m deep. A hose delivers 1515 L per minute. How long to fill the tank?

  1. Volume: V=2×1.5×1.2=3.6V = 2 \times 1.5 \times 1.2 = 3.6 m3^3 =3600= 3600 L.
  2. Time: t=360015=240t = \dfrac{3600}{15} = 240 min =4= 4 hours.

Practice: Year 8 core

Fluency

Volume of right prisms

    1. Find the volume of a cuboid 7×4×37 \times 4 \times 3 cm.
    2. Find the volume of a cube of side 66 cm.
    3. Find the volume of a triangular prism with triangle base 1010 cm, height 66 cm, and length 1515 cm.
    4. Find the volume of a trapezoidal prism: parallel sides 44 m and 66 m, height 33 m, length 88 m.
    5. A cuboid has volume 480480 cm3^3 and a base of 8×58 \times 5 cm. Find its height.
    6. A triangular prism has volume 150150 cm3^3 and length 1010 cm. Find the area of its triangular base.
Fluency

Volume and capacity

    1. Convert 35003500 mL to L.
    2. Convert 4.24.2 L to mL.
    3. Convert 0.750.75 m3^3 to L.
    4. Convert 23002300 cm3^3 to mL.
    5. A fish tank is 60×30×4060 \times 30 \times 40 cm. What is its capacity in L?
    6. A pool is 1212 m by 66 m by 1.51.5 m. How many kL?
Fluency

Rates and time

    1. A 300300 L tank fills at 55 L/min. How long?
    2. A hose delivers 0.20.2 L/s. How long (minutes) to fill a 6060 L drum?
    3. A pool of 90 00090\,000 L is filled at 150150 L/min. How many hours?
    4. A dripping tap loses 44 drops/sec and 2020 drops = 11 mL. How much water in a day (L)?
Reasoning

Explain and spot the mistake

    1. Liam writes the volume of a 22 cm cube as 88 cm2^2. What is the error?
    2. Two cuboids have the same volume. Must they have the same surface area? Give a reason.
    3. Explain why 11 cm3=1^3 = 1 mL using the definition of the metric system.
    4. A tap flows at 1212 L/min. Without calculating, decide whether a 10001000 L tank fills in under or over 11 hour. Justify.
Problem solving

Real contexts

    1. A water tank is 1.21.2 m by 0.80.8 m by 1.51.5 m deep. A hose delivers 2020 L/min. How long to fill?
    2. A swimming pool is 1515 m by 88 m with uniform depth 1.41.4 m. If water costs $2.40/kL, find the total fill cost.
    3. A shoebox is 3333 cm by 2222 cm by 1515 cm. Give its volume in cm3^3 and in litres (to 2 dp).
    4. A chocolate bar in the shape of a triangular prism has equilateral cross-section (side 33 cm, approximate height 2.62.6 cm) and length 1010 cm. Find its volume (to the nearest cm3^3).

Challenge

Reasoning

Harder problems

    1. A cube has surface area 150150 cm2^2. Find its volume.
    2. Two identical right-angled triangular prisms are joined along their rectangular faces to form a cuboid. If each prism has legs 33 cm and 44 cm and length 1010 cm, find the volume of the cuboid.
    3. A rectangular tank (22 m × 11 m × 11 m) is being filled at 2525 L/min while draining at 1010 L/min. How long to fill if both taps are open?
    4. A glass is a cylinder of radius 33 cm and height 1010 cm. Find its capacity in mL. (Use V=πr2hV = \pi r^2 h; π≈3.14\pi \approx 3.14.)
Year 8 Mathematics study companion | Practice