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Task Planning & Logistics · Guided Practice

3D Container Packing

10 questions with answers and video solutions. Try each one before revealing the answer.

1
A shelf is 120\displaystyle 120 cm long.
Boxes are 25\displaystyle 25 cm wide.
Calculate how many boxes fit along the shelf.
Video solution coming soon
2
A crate has internal dimensions 60\displaystyle 60 cm by 45\displaystyle 45 cm by 30\displaystyle 30 cm.
Boxes measure 20\displaystyle 20 cm by 15\displaystyle 15 cm by 10\displaystyle 10 cm and must be packed in this orientation.
Calculate how many boxes fit in the crate.
Video solution coming soon
3
A crate has internal dimensions 100\displaystyle 100 cm by 80\displaystyle 80 cm by 60\displaystyle 60 cm.
Cartons measure 25\displaystyle 25 cm by 20\displaystyle 20 cm by 15\displaystyle 15 cm and must be packed in this orientation.
Calculate how many cartons fit in the crate.
Video solution coming soon
4
A van has an internal load space of 300\displaystyle 300 cm by 180\displaystyle 180 cm by 200\displaystyle 200 cm.
Boxes measure 50\displaystyle 50 cm by 40\displaystyle 40 cm by 40\displaystyle 40 cm and must be packed upright in this orientation.
Calculate how many boxes fit in the van.
Video solution coming soon
5
A crate has internal dimensions 90\displaystyle 90 cm by 60\displaystyle 60 cm by 45\displaystyle 45 cm.
Boxes measure 30\displaystyle 30 cm by 20\displaystyle 20 cm by 15\displaystyle 15 cm and must be packed in this orientation.
Calculate how many boxes fit in the crate.
Video solution coming soon
6
2019 P2 Q9(c)
3 Marks

The books are to be packed in boxes for transporting to the bookshops. The dimensions of the book and the internal dimensions of the box are shown in the diagrams.

Diagram showing dimensions of a single book and a packing boxDiagram showing book and box dimensions

The books need to be laid with the front cover facing upwards in the boxes. They must all be aligned in the same direction.

(c) Calculate the maximum number of books that can be packed into each box.

7
2021 P2 Q9(c)
3 Marks

The packets are in the shape of a cuboid with external dimensions as shown.

Cuboid packet measuring 2cm by 2cm by 5.5cm

For delivery, the packets of sweets are packed into a box with internal dimensions as shown.

Delivery box measuring 50cm by 30cm by 15cm

All the packets must be aligned in the same direction.

(c) Calculate the maximum number of packets that can fit in the box.

8
2023 P1 Q7
2 Marks

Biscuits are sold in tins in the shape of a cuboid as shown.

Biscuit tin measuring 15 cm by 10 cm by 10 cm

The tins need to be packed into boxes with the lid facing upwards.

There are two types of box available with internal measurements as shown.

Box A measuring 50 cm by 51 cm by 42 cm

Determine the maximum number of tins which can be packed. Use your working to justify your answer.

9
2024 P1 Q8
3 Marks

Tabitha is a van driver for a supermarket that provides home deliveries.
Orders are packed into boxes for home delivery to customers.

The dimensions of each box and the internal dimensions of the van are shown in the diagrams.

Diagram of a box with dimensions 60 cm by 40 cm by 20 cm Diagram of a van with internal dimensions 410 cm length, 220 cm height, 190 cm width

All boxes must be aligned in the same direction.
Calculate the maximum number of boxes that will fit in the van.

10
2025 P2 Q5(b)
3 Marks

The boxes are packed into crates for transportation.
The boxes must be aligned in the same direction.

Box with a 'this way up' arrow pointing along the 8.6 cm side

The internal dimensions of a crate are shown.

Crate with dimensions 100 cm by 75 cm by 40 cm

(b) Calculate the maximum number of boxes that can be packed into a crate.

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