Nets & views of 3-D objects

Imagine folding and unfolding a solid.

Learning goal

A net unfolds the surface

Connect faces in a valid net to the solid and distinguish top, front and side views.

A net is a connected arrangement of faces that folds into a solid without gaps or overlaps. For a closed prism every face appears exactly once.

Predict · change · explain

Explore the dimensions

Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.

Track the edges

Edges that meet when folded must have equal lengths. Opposite rectangular-prism faces are congruent, but many different arrangements can make a valid net.

Views show one direction

A front, top or side view is a two-dimensional projection. It can hide depth, so more than one view may be needed to identify a solid.

Follow the reasoning

Worked examples

How many faces does a closed rectangular prism have?

  1. Count two bases and four side faces.
  2. A closed net has six rectangles; a lidless container has five faces.

A cube has edges of 3 cm.

  1. Each square face has area 3 × 3 = 9 cm².
  2. Six faces cover 54 cm² in total.

Guided Practice

A rectangular box has no lid. How many faces appear in its net?

A first hint

Count the bottom and the walls.

Compare your reasoning

Five: one bottom and four side faces.

Practice

Fresh questions · useful feedback

Build fluency, one decision at a time.

Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.

0 of 8 questions completed

Enter a number, decimal or fraction such as −3/2. Leave out units and π. If asked for k in kπ, enter only k.

This round saves on this device. It is practice, not a school mark.

Connections

Sketch two different cube nets and explain how you checked the folds.

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