Geometry

Match each three-dimensional figure with its net.

Step-by-step solution with explanation

Final Answer

Cube ↔ net of 6 equal squares; Rectangular Prism ↔ net of 6 rectangles in 3 pairs; Triangular Prism ↔ net of 2 triangles + 3 rectangles; Square Pyramid ↔ net of 1 square + 4 triangles; Cylinder ↔ net of 2 circles + 1 rectangle; Cone ↔ net of 1 circle + 1 curved sector

Step-by-step solution

1

Identify common 3D figures and nets

A net is a flat pattern that folds up to make a 3D shape. We match each shape by counting its faces and recognizing their types.
2

Match the cube to its net

A cube has 6 square faces. Its net shows exactly 6 squares arranged in a cross or T-shape that fold up to close on all sides.
3

Match the rectangular prism to its net

A rectangular prism has 6 rectangular faces in 3 matched pairs. Its net shows these rectangles laid out flat so opposite faces are equal in size.
4

Match the triangular prism to its net

A triangular prism has 2 triangular ends and 3 rectangular sides. Its net shows 2 triangles on the top and bottom with 3 rectangles running along the middle strip.
5

Match the square pyramid to its net

A square pyramid has 1 square base and 4 triangular faces. Its net shows the square in the center with one triangle attached to each side of the square.
6

Match the cone and cylinder to their nets

A cone's net is a circle (base) plus a fan-shaped sector. A cylinder's net is two circles (top and bottom) plus one rectangle that wraps around the side.

Understanding this problem

Learning Insight

A net works because every face of the 3D shape must appear exactly once in the flat pattern. Counting faces and matching their shapes (triangles, squares, rectangles, circles) is the key concept — the net is just those faces 'unfolded' into one connected flat piece.

Quick Tip

Count the faces first! If you see 2 triangles and 3 rectangles, it must be a triangular prism. If you see 1 square and 4 triangles, it must be a square pyramid. The face count never lies.

Common Mistake

Students often confuse a square pyramid net (1 square + 4 triangles) with a triangular pyramid/tetrahedron net (4 triangles only, no square). Always check whether the base face is a square or a triangle.