Problem Solving with Cuboids

In this lesson, five problems link the volume of cuboids to:

  • Ratio
  • 3D coordinates
  • Standard form
  • Setting up and solving equations
  • Converting between metric units

Throughout the lesson, I asked students to sketch the diagrams so they could label the critical information. Then, I encourage them to work together to share their approaches to each problem and question each other. While most calculations are reasonably simple, I remind students to use a calculator to focus on problem-solving rather than arithmetic.

I recommend teaching this lesson as part of the schemes of work on perimeter, area and volume in key stage 3 or volume and surface area in Key Stage 4.

Problem Solving with Cuboids and 3D Coordinates

Problem Solving with Cuboids

Finding a length when given the volume and area is a common question when learning about cuboids. This question takes the idea up another level by challenging students to find the cross-section area from two 3D coordinates and use the calculated length to find the third coordinate.

If students struggle to get started, I encourage them to sketch the cuboid without the grid and note the cross-sectional area and length FE.

Next, I prompt them to label coordinates C and F on the diagram to find the area of face BFGC.

Problem Solving with Cuboids and Ratio

I’ve yet to find a topic that can not be linked to ratio in sIn this question, students consider which two parts of a three-part ratio combine to give the smallest area.

Most students correctly identify the numbers 2 : 3 but often struggle knowing how to use them to give the area of 150 cm2. If this happens, I encourage them to think about equivalent ratios, for instance, 4 : 6 or 6 : 9 and so on.

Problem Solving with Cuboids and Unknowns

Problem Solving with Cuboids

In my experience, because there is limited information, students find this question the most challenging. Therefore, I encourage them to begin by finding the length of the pink cube.

Next, they need to consider what changes and remains the same without the blue cuboid. When students realise both shapes have the same height, they can find the blue cross-sectional area. From this, go on to work out x.

Share this article


About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

Related Lessons

Ages 14 - 16
Surface Area of Square Based Pyramids
Ages 11 - 13
Total Surface Area of Cylinders
Ages 14 - 16
Volume of a Cone
Ages 11 - 13
Volume of a Cylinder

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.