Now try to make the above shapes using straws and plasticine/thread and fill in the table. Shapes Number of faces (F) Number of corners (V) Number of edges (E) Cube/Square Prism ? ? ? Cuboid/Rectangular Prism ? ? ? Triangular Pyramid ? ? ? Square Pyramid ? ? ? Triangular Prism ? ? ?

Make each skeleton first: a straw is an edge and a lump of plasticine is a corner . Then count. How to count without missing anything Corners — count the lumps of plasticine. Edges — count the straws. Faces — count the flat windows the straws close in; do not forget the bottom and the back. The completed table: Shapes Number of faces (F) Number of corners (V) Number of edges (E) Cube/Square Prism 6 8 12 Cuboid/Rectangular Prism 6 8 12 Triangular Pyramid 4 4 6 Square Pyramid 5 5 8 Triangular Prism 5 6 9 Cube: top and bottom + 4 sides = 6 faces. 4 corners on top and 4 below = 8 corners. 4 straws on top, 4 below and 4 standing up = 12 edges. Triangular prism: 2 triangles + 3 rectangles = 5 faces; 3 corners on top and 3 below = 6 corners; 3 + 3 + 3 = 9 edges. Why it happens: Every straw is one edge, every lump is one corner, and every closed loop of straws holds one flat face. So building the skeleton and counting is the surest way.

Identify any relationship that you may find between the number of faces (F), edges (E), and corners (V). Calculate F+V–E in each case. What do you notice? Shapes Number of faces (F) Number of corners (V) Number of edges (E) Cube/Square Prism ? ? ? Cuboid/Rectangular Prism ? ? ? Triangular Pyramid ?

Work out F + V – E for each shape, one at a time. Shape F V E F + V – E Cube / Square prism 6 8 12 6 + 8 – 12 = 2 Cuboid / Rectangular prism 6 8 12 6 + 8 – 12 = 2 Triangular pyramid 4 4 6 4 + 4 – 6 = 2 Square pyramid 5 5 8 5 + 5 – 8 = 2 Triangular prism 5 6 9 5 + 6 – 9 = 2 What I notice: the answer is 2 every single time . F + V – E = 2 Why it happens: In every one of these solids the faces, corners and edges fit together in the same way, so the three numbers always balance out to 2. Try it on a hexagonal prism: F = 8, V = 12, E = 18, and 8 + 12 – 18 = 2 again.

Sort 3D shapes by the number of flat faces. Write their names here. Number of faces 1 flat face 2 flat faces 4 flat faces 5 flat faces 6 flat faces 8 flat faces Name of the shape

Number of faces 1 flat face 2 flat faces 4 flat faces 5 flat faces 6 flat faces 8 flat faces Name of the shape cone cylinder triangular pyramid square pyramid, triangular prism cube, cuboid hexagonal prism How each one was counted Cone — only the round flat bottom is flat, so 1 flat face. Cylinder — the flat circle on top and the one below, so 2 flat faces. Triangular pyramid — 3 slanting triangles + 1 base = 4. Square pyramid — 4 triangles + 1 square base = 5. Triangular prism — 3 rectangles + 2 triangles = 5. Cube and cuboid — top, bottom and 4 sides = 6. Hexagonal prism — 6 rectangles + 2 hexagons = 8. Tip: The sphere is not in the table at all, because it has no flat face — it is curved all over.

NCERT Solutions for Class 4th Maths Chapter 1 Making the shapes with straws and plasticine; sorting 3D shapes — In-text Questions

Book page 4 Updated on2026-09-19

Q1.

Now try to make the above shapes using straws and plasticine/thread and fill in the table.

Shapes	Number of faces (F)	Number of corners (V)	Number of edges (E)
Cube/Square Prism	?	?	?
Cuboid/Rectangular Prism	?	?	?
Triangular Pyramid	?	?	?
Square Pyramid	?	?	?
Triangular Prism	?	?	?

Answer

Make each skeleton first: a straw is an edge and a lump of plasticine is a corner. Then count.

How to count without missing anything

Corners — count the lumps of plasticine.
Edges — count the straws.
Faces — count the flat windows the straws close in; do not forget the bottom and the back.

The completed table:

Shapes	Number of faces (F)	Number of corners (V)	Number of edges (E)
Cube/Square Prism	6	8	12
Cuboid/Rectangular Prism	6	8	12
Triangular Pyramid	4	4	6
Square Pyramid	5	5	8
Triangular Prism	5	6	9

Cube: top and bottom + 4 sides = 6 faces. 4 corners on top and 4 below = 8 corners. 4 straws on top, 4 below and 4 standing up = 12 edges.

Triangular prism: 2 triangles + 3 rectangles = 5 faces; 3 corners on top and 3 below = 6 corners; 3 + 3 + 3 = 9 edges.

Why it happens: Every straw is one edge, every lump is one corner, and every closed loop of straws holds one flat face. So building the skeleton and counting is the surest way.

Q2.

Identify any relationship that you may find between the number of faces (F), edges (E), and corners (V). Calculate F+V–E in each case. What do you notice?

Shapes	Number of faces (F)	Number of corners (V)	Number of edges (E)
Cube/Square Prism	?	?	?
Cuboid/Rectangular Prism	?	?	?
Triangular Pyramid	?	?	?
Square Pyramid	?	?	?
Triangular Prism	?	?	?

Answer

Work out F + V – E for each shape, one at a time.

Shape	F	V	E	F + V – E
Cube / Square prism	6	8	12	6 + 8 – 12 = 2
Cuboid / Rectangular prism	6	8	12	6 + 8 – 12 = 2
Triangular pyramid	4	4	6	4 + 4 – 6 = 2
Square pyramid	5	5	8	5 + 5 – 8 = 2
Triangular prism	5	6	9	5 + 6 – 9 = 2

What I notice: the answer is 2 every single time.

F + V – E = 2

Why it happens: In every one of these solids the faces, corners and edges fit together in the same way, so the three numbers always balance out to 2. Try it on a hexagonal prism: F = 8, V = 12, E = 18, and 8 + 12 – 18 = 2 again.

Q3.

Sort 3D shapes by the number of flat faces. Write their names here.

Number of faces	1 flat face	2 flat faces	4 flat faces	5 flat faces	6 flat faces	8 flat faces
Name of the shape

Answer

Number of faces	1 flat face	2 flat faces	4 flat faces	5 flat faces	6 flat faces	8 flat faces
Name of the shape	cone	cylinder	triangular pyramid	square pyramid, triangular prism	cube, cuboid	hexagonal prism

How each one was counted

Cone — only the round flat bottom is flat, so 1 flat face.
Cylinder — the flat circle on top and the one below, so 2 flat faces.
Triangular pyramid — 3 slanting triangles + 1 base = 4.
Square pyramid — 4 triangles + 1 square base = 5. Triangular prism — 3 rectangles + 2 triangles = 5.
Cube and cuboid — top, bottom and 4 sides = 6.
Hexagonal prism — 6 rectangles + 2 hexagons = 8.

Tip: The sphere is not in the table at all, because it has no flat face — it is curved all over.

Q4.

Can you construct a 3D shape with 3 flat faces?

Answer

Yes — but it must have a curved face as well.

Cut a cylinder straight down the middle, along its length.
Half a cylinder has 3 flat faces: one rectangle where you cut, and two half-circles at the two ends.
It also has one curved face, which is the outside of the cylinder.

With flat faces only, 3 is not possible. The smallest solid made of flat faces alone is the triangular pyramid, and that already needs 4 faces.

Why it happens: Three flat faces cannot close up a space on their own — there is always a gap left, so either a fourth flat face or a curved face is needed.

Q5.

Now sort 3D shapes by the number of straight edges. Write their names here.

Number of edges	6 straight edges	8 straight edges	9 straight edges	12 straight edges
Name of the shape

Answer

Number of edges	6 straight edges	8 straight edges	9 straight edges	12 straight edges
Name of the shape	triangular pyramid	square pyramid	triangular prism	cube, cuboid

How each one was counted

Triangular pyramid: 3 edges of the base + 3 slanting edges = 6
Square pyramid: 4 edges of the base + 4 slanting edges = 8
Triangular prism: 3 on top + 3 below + 3 standing up = 9
Cube / cuboid: 4 on top + 4 below + 4 standing up = 12

Tip: The cylinder and the cone are not here. Their edges are curved, not straight, so they do not belong in a table of straight edges.

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