Volumes Cubes and Cuboids 2

Shape and space part 1 MSS1/L1.2

VOLUMES CUBES AND CUBOIDS 2

To find the volume of a cube/cuboid, multiply: length x width x height

Example:

What is the volume of a child’s shoe box 20cm long, 10cm wide and 8cm high? Volume = length x width x height = 20 x 10 x 8cm³ = 200 x 8cm³ = 1600cm ³

Note - the volume of an empty shape may be called the cubic capacity.

A) Try finding these volumes (the answers will be in cubic units eg cm³, m³ etc)

2cm 9cm

1 Shape and space part 1 MSS1/L1.2

4) 5cm 6cm

9cm 20cm

6) A ring case measures 3cm by 3cm and is 2cm high. What is it’s volume in cm³?

7) A square shaped tube is 85cm high, and has a length and width of 5cm each way. What is it’s capacity?

8) A room in a club is 9m wide, 26m long and 4m high. What is it’s volume?

9) A car radio speaker is 18cm wide, 9cm deep and 10cm high. What volume is it?

10) A plant container is in the shape of a cube with a side length of 9cm. What capacity does it have?

11) Joanne thinks a cube with sides of 8cm holds more than a cuboid with sides of 6, 8 and 10cm. Is she right?

LONG MULTIPLICATION AND DECIMAL FRACTIONS

You may need to do long multiplication.

Example: What is the volume of a box with dimensions 35cm by 25cm by 8cm? Multiply length x width 35 x 25 175 700  don’t forget the 0 875

Now multiply by the height 875 x 8 7000

Answer = 7000cm ³

You may have to multiply decimal fractions.

Example:

A room is 5.6m long, 4m wide and 3m high. What is it’s volume?

length x width 5.6 x height 22.4 x 4 x 3 22.4 67.2 2 1 The volume is 67.2m ³

B) Try these questions.

1) A baking tray measures 25cm x 30cm x 5cm. What is it’s volume in cm³? Another tray measures 25cm by 25cm by 6cm. Which tray holds more?

2) Find the volume of these jewellery cases, in cubic centimetres.

Length Width Height a) 4cm 2cm 3.5cm ◘ b) 6.2cm 3cm 5cm c) 5.5cm 8cm 14cm

3) What is the volume of a Weetabix packet which measures 25cm by 20cm by 5cm?

4) What is the volume of a matchbox which measures 11cm by 6.4cm by 3cm?

5) Small boxes measuring 3cm by 2cm by 1cm are packed into a large box which measures 15cm by 12cm by 10cm. What is the volume of: a) the small boxes? b) the large box? c) How many small boxes will fit into the large box?

6) Ice cubes which measure 2cm by 2cm by 2cm are made with water from a container 16cm by 13cm by 8cm. How many can be made?

7) Crates which measure 1.5m by 2m by 2m are packed in a large container 9m by 4m by 3m. How many can be packed in?

You may need to do long multiplication with a decimal fraction.

Example:

A shoulder bag is 8.5cm by 21cm by 9cm. What is it’s cubic capacity?

85 8.5  1 decimal place 178.5 x 21 x 21 x 9 85 85 1606.5 1700 1700 7 7 4 1785 178.5  1 decimal place

Answer = 1606 5cm ³

C) Try finding these volumes.

1) What is the volume of these music speakers?

Length Width Height a) 25cm 20cm 35cm b) 18.2 16cm 30cm c) 9cm 9.5 15cm

2) Nina is checking on the cubic capacity of different freezing compartments in fridges.

The first model has a compartment measuring 9.5cm by 30cm by 40cm.

The second compartment measures 21.5cm x 18cm x 30cm.

Which has the larger capacity?

Check your answers, then discuss with your tutor what you need to work on next.

Answers

Volume Cubes And Cuboids 2

1) 45m³ 1) 3750cm³ 3750cm³ 2) 54m³ same 3) 125m³ 2) a) 28cm³ 4) 540cm³ b) 93cm³ 5) 1800cm³ c) 616cm³

6) 18cm³ 3) 2500cm³

7) 2125cm³ 4) 211.2cm³

8) 936m³ 5) a) 6cm³ b) 1800cm³ 9) 1620cm³ c) 300 10) 729cm³ 6) 1664  8 = 208 ice cubes 11) 512cm³ 7) 108  6 = 18 crates 480cm³ She is right C)

1) a) 17500cm³ b) 8736cm³ c) 1282.5cm³

2) 11400cm³ 11610cm³ the second