Nets of Cuboids
Semester 4B · Chapter 17 · Lesson 2 · MATH-4B-C17-L02
Before you begin: prerequisite check
Recall: 17.01; 2D rectangles. Attempt these questions independently first.
A 4 cm by 11 cm by 6 cm cuboid has how many faces, edges, and vertices?
Show answer and reasoning
Count six rectangular faces, twelve meeting segments and eight corner points.
A 12-cm tall cuboid has 6 faces. How many edges must it have, regardless of side lengths?
Show answer and reasoning
A cuboid always has twelve edges: four in each of three directions.
Does a 13-cm long rectangular box have 8 or 12 vertices? Explain.
Show answer and reasoning
A vertex is a corner; there are four corners on each of two opposite rectangular ends.
Key vocabulary
- cuboid
- solid with six rectangular faces
- face
- flat rectangular side of a cuboid
- edge
- segment where two faces meet
- vertex
- point where edges meet
- net
- connected plane arrangement of faces that folds into a solid
Understand the concept
A net is a connected arrangement of flat faces that can fold into a solid without overlap. A cuboid has three pairs of congruent opposite rectangles. For dimensions 2 by 3 by 4, the faces are two 2-by-3 rectangles, two 2-by-4 rectangles, and two 3-by-4 rectangles. A correct net must contain all six and join matching edges so they can fold into one solid. A drawing with the right total number of faces may still be invalid if the faces overlap after folding.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
A cuboid measures 5 cm by 3 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Check 1: try it yourself
A cuboid measures 2 cm by 6 cm by 5 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Worked example 2
A cuboid measures 2 cm by 4 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Check 2: try it yourself
A cuboid measures 4 cm by 2 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Worked example 3
Draw one connected, foldable six-face net of a 6 cm by 4 cm by 3 cm cuboid. Label each face with its dimensions.
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Check 3: try it yourself
Draw one connected, foldable six-face net of a 3 cm by 6 cm by 5 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Guided practice
A cuboid measures 2 cm by 6 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid measures 5 cm by 6 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Draw one connected, foldable six-face net of a 2 cm by 6 cm by 5 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Draw one connected, foldable six-face net of a 4 cm by 2 cm by 5 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
A learner draws six correct rectangles for a 5×2×3 cuboid but leaves them as six unconnected pieces. Is that a complete net? Explain.
Show answer and reasoning
Matching face sizes are necessary but not sufficient: a net is a connected planar arrangement that folds into the cuboid.
Independent practice
A cuboid measures 6 cm by 2 cm by 4 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid measures 5 cm by 4 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Draw one connected, foldable six-face net of a 3 cm by 5 cm by 2 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Draw one connected, foldable six-face net of a 4 cm by 5 cm by 2 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
A learner draws six correct rectangles for a 2×6×3 cuboid but leaves them as six unconnected pieces. Is that a complete net? Explain.
Show answer and reasoning
Matching face sizes are necessary but not sufficient: a net is a connected planar arrangement that folds into the cuboid.
A cuboid measures 4 cm by 3 cm by 6 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid measures 3 cm by 2 cm by 4 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Draw one connected, foldable six-face net of a 4 cm by 6 cm by 3 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
A cuboid measures 4 cm by 6 cm by 2 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A learner claims: “Any six rectangles with the correct side lengths count as a valid cuboid net even if disconnected.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: a net must be connected and fold without overlap into the solid. Explain the relevant quantities or properties, not merely the final answer.
Exit check
A cuboid measures 2 cm by 5 cm by 3 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
A cuboid measures 4 cm by 2 cm by 5 cm. List the dimensions of its six faces, including repeated face sizes.
Show answer and reasoning
Opposite faces come in matching pairs, so there are two of each of the three face sizes.
Draw one connected, foldable six-face net of a 3 cm by 5 cm by 4 cm cuboid. Label each face with its dimensions.
Show answer and reasoning
One valid arrangement uses a connected strip of four side faces, plus two matching end faces attached without overlap. Other foldable nets are also correct.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.