NCERT Solutions for Class 4th Maths Chapter 1 Completing cubes, and matching solids to their descriptions — Drawing Cubes on a Triangular Dot Paper
Book page 8 Updated on2026-09-19
Q1.
Can you complete the following cubes?
The triangular dot paper from the book: one cube is complete, the other two are only started.
Answer
Yes. On triangular dot paper a cube is drawn as a
six-sided figure with three lines meeting at the centre.
Steps
Look at the finished cube on the left. Count: its outline has 6 sides, and 3
lines run from the middle point to three of the corners.
In the unfinished drawings, first close the outline — join dot to dot until you
have those 6 sides.
Then mark the middle dot and draw the 3 lines from it to alternate corners.
Every line must go from one dot to the next dot, never across the paper.
Each finished picture shows 3 faces of the cube — the top, the left and the
right. The other 3 faces are hidden behind.
Why it happens: On triangular dot paper the dots lie in three
slanting directions. Those are exactly the three directions of the edges of a cube, so a
cube fits the paper neatly.
Q2.
Match the pictures to the descriptions and name the shapes. a) I have 5 faces and 5 corners. I have 8 edges. 1 of my faces is a square and 4 of my faces are triangles.………. b) I have 1 flat face, 1 curved face, and 1 edge.………. c) I have 1 curved face. I have no edges or corners.……. d) I have 2 flat faces, 1 curved face, and 2 edges. I have no corners.………. e) I have 5 faces, 6 corners, and 9 edges, and 2 of my faces are triangles.………. f) I have 6 faces, 12 edges, and 8 corners.……….
The seven pictures printed down the side of the page.
Answer
Take one clue at a time — the number of faces, then the corners, then
the edges.
Description
Name of the shape
Picture
a) 5 faces, 5 corners, 8 edges, 1 square and 4 triangles
e) 5 faces, 6 corners, 9 edges, 2 of them triangles
triangular prism
(7)
f) 6 faces, 12 edges, 8 corners
cube (the cuboid also fits)
(6)
The seven pictures with their names.
Note: description (f) fits the cube and the
cuboid equally well — both have 6 faces, 12 edges and 8 corners. The picture
left over is the cuboid (4), so the cube is the better match for (f).
Why it happens: (a) has one square and four triangles meeting at
a point, which can only be a square pyramid. (b) and (d) have a curved face, so they are
the cone and the cylinder: the cone has one rim, the cylinder has two.
Q3.
Each one is different. How? Discuss.
The five solids printed at the bottom of the page.
Answer
Each solid differs in its faces, its edges and its corners.
Shape
Faces
Corners
Edges
What makes it different
1. Sphere
1 curved
0
0
round everywhere; it rolls in every direction
2. Cone
1 flat + 1 curved
1
1 curved
one sharp point on top
3. Triangular pyramid
4 triangles
4
6
all faces are triangles
4. Cube
6 equal squares
8
12
all six faces are the same size
5. Cuboid
6 rectangles
8
12
long faces and short faces, not all alike
Other differences you can feel and see
The sphere rolls in any direction; the cone rolls only round in a circle; the
cube and cuboid do not roll at all.
The cube and the cuboid can be stacked; the sphere and the cone cannot be stacked
easily.
The cube and the cuboid have the same numbers, yet they look different, because the
cube’s faces are all equal squares.
Why it happens: A curved face lets a shape roll; flat faces let
it sit still and be stacked. That is why round things and box-shaped things behave so
differently.