Volume of prisms

Find the volume of rectangular and triangular prisms, and solve capacity and composite prism problems.

Worked examples

Volume of a rectangular prism

Straightforward

Problem

A rectangular prism has length

4 \text{ cm}

, width

6 \text{ cm}

and height

5 \text{ cm}

. Find its volume.

Volume of a triangular prism

Moderate

Problem

A triangular prism has a right-angled triangular cross-section with base

8 \text{ cm}

and perpendicular height

3 \text{ cm}

. The prism is

7 \text{ cm}

long. Find its volume.

Volume of a tank and capacity

Challenging

Problem

A rectangular water tank is

90 \text{ cm}

long,

60 \text{ cm}

wide and

50 \text{ cm}

deep. Water fills

\tfrac{3}{4}

of its capacity. How many litres of water are in the tank? (

1 \text{ litre} = 1000 \text{ cm}^3

)

Practise

Q1·Straightforward

A rectangular prism has length

5 \text{ cm}

, width

3 \text{ cm}

and height

4 \text{ cm}

. Find its volume in

\text{cm}^3

Q2·Straightforward

A rectangular prism has length

8 \text{ cm}

, width

2 \text{ cm}

and height

3 \text{ cm}

. Find its volume in

\text{cm}^3

Q3·Straightforward

A rectangular prism has length

6 \text{ cm}

, width

4 \text{ cm}

and height

5 \text{ cm}

. Find its volume in

\text{cm}^3

Q4·Straightforward

A rectangular prism has length

7 \text{ cm}

, width

4 \text{ cm}

and height

2 \text{ cm}

. Find its volume in

\text{cm}^3

Q5·Moderate

A triangular prism has a right-angled triangular cross-section with base

6 \text{ cm}

and perpendicular height

4 \text{ cm}

. The prism is

10 \text{ cm}

long. Find its volume in

\text{cm}^3

Q6·Moderate

A triangular prism has a right-angled triangular cross-section with base

8 \text{ cm}

and perpendicular height

3 \text{ cm}

. The prism is

7 \text{ cm}

long. Find its volume in

\text{cm}^3

Q7·Moderate

A triangular prism has a right-angled triangular cross-section with base

5 \text{ cm}

and perpendicular height

6 \text{ cm}

. The prism is

9 \text{ cm}

long. Find its volume in

\text{cm}^3

Q8·Moderate

A triangular prism has a right-angled triangular cross-section with base

10 \text{ cm}

and perpendicular height

4 \text{ cm}

. The prism is

8 \text{ cm}

long. Find its volume in

\text{cm}^3

Q9·Challenging

A prism has an L-shaped cross-section formed by joining a

6 \text{ cm} \times 4 \text{ cm}

rectangle and a

3 \text{ cm} \times 2 \text{ cm}

rectangle. The prism is

8 \text{ cm}

long. Find its volume in

\text{cm}^3

Q10·Challenging

A rectangular water tank is

60 \text{ cm}

long,

25 \text{ cm}

wide and

30 \text{ cm}

deep. Water fills

\tfrac{3}{4}

of its capacity. How many litres of water are in the tank? (

1 \text{ litre} = 1000 \text{ cm}^3

)

Q11·Challenging

A building has a cross-section made up of a rectangle

5 \text{ m}

wide and

3 \text{ m}

tall, topped by a triangle

5 \text{ m}

wide and

2 \text{ m}

tall. The building is

8 \text{ m}

long. Find the total volume in

\text{m}^3

Q12·Challenging

A concrete ramp has a trapezoidal cross-section with parallel sides of

0.5 \text{ m}

and

2 \text{ m}

, and a perpendicular width of

3 \text{ m}

. The ramp is

5 \text{ m}

long. Find the volume of concrete in

\text{m}^3