Here are three views of a cube. Can you draw them on the net in the correct order? View 1 View 2 View 3 Three views of the same cube, and the net to draw them on.

First find which faces are opposite each other , then put opposite faces in opposite places on the net. The three pictures show five different faces: purple face with a green square sky-blue face with a yellow circle cream face with a red cross pink face with a blue star plain brown face Working out the opposite pairs List what you can see touching what. View 1: purple, blue and cream meet at a corner. View 2: purple, cream and pink meet. View 3: brown, blue and cream meet. The cream face touches four different faces — purple, blue, pink and brown. A face has only 4 neighbours, so the face opposite the cream one is the sixth face , which is never shown in any picture. Compare views 1 and 3. Both show the blue face and the cream face together, but one has purple on top and the other has brown on top. Only two faces of a cube touch both blue and cream — the two at the ends of the edge where blue and cream meet — and those two faces are opposite each other. So purple is opposite brown . Two pairs are now fixed , so the two faces left over must be the third pair: blue is opposite pink . purple with green square ↔ plain brown sky-blue with yellow circle ↔ pink with blue star cream with red cross ↔ the sixth face (never shown) Now fill the net. On this cross-shaped net, the 1st and 3rd squares of the long row are opposite each other, the 2nd and 4th are opposite each other, and the top square is opposite the bottom one. purple blue sixth face pin

NCERT Solutions for Class 5th Maths Chapter 7 Views and nets, hollow cube frames, and Nisha's painted cube — Cube Connections

Book page 102 Updated on2026-09-19

Q1.

Here are three views of a cube. Can you draw them on the net in the correct order?

Three views of the same cube, and the net to draw them on.

Answer

First find which faces are opposite each other, then put opposite faces in opposite places on the net.

The three pictures show five different faces:

purple face with a green square
sky-blue face with a yellow circle
cream face with a red cross
pink face with a blue star
plain brown face

Working out the opposite pairs

List what you can see touching what. View 1: purple, blue and cream meet at a corner. View 2: purple, cream and pink meet. View 3: brown, blue and cream meet.
The cream face touches four different faces — purple, blue, pink and brown. A face has only 4 neighbours, so the face opposite the cream one is the sixth face, which is never shown in any picture.
Compare views 1 and 3. Both show the blue face and the cream face together, but one has purple on top and the other has brown on top. Only two faces of a cube touch both blue and cream — the two at the ends of the edge where blue and cream meet — and those two faces are opposite each other. So purple is opposite brown.
Two pairs are now fixed, so the two faces left over must be the third pair: blue is opposite pink.

purple with green square ↔ plain brown
sky-blue with yellow circle ↔ pink with blue star
cream with red cross ↔ the sixth face (never shown)

Now fill the net. On this cross-shaped net, the 1st and 3rd squares of the long row are opposite each other, the 2nd and 4th are opposite each other, and the top square is opposite the bottom one.

Purple faces brown, blue faces pink, cream faces the sixth square — which no view shows, so draw your own design there.

Why opposite faces must go in those places: Fold the net up in your mind. The 1st square of the row swings round to sit exactly across from the 3rd; the 2nd sits across from the 4th; and the top flap ends up across from the bottom flap. So faces that must be opposite on the cube have to be in those paired places on the net.

Check it yourself: Copy the net, draw the designs, cut it out and fold it into a cube. Then turn your cube until it looks like each of the three pictures in the book.

Q2.

Here are some big solid cube frames. How many small cubes have been removed from each cube? (a) (b) (c)

Answer

(a) 7 small cubes (b) 32 small cubes (c) 81 small cubes.

In each picture only the edges of the big cube are left standing. Everything else — the middle of each face and the whole inside — has been taken out.

The method (use it for any size)

Count the small cubes in the whole solid cube. Multiply the side by itself three times.
Count the small cubes that are left in the frame: 8 corner cubes, plus the cubes along the 12 edges.
Subtract. Removed = whole − left.

Cube	Size	Small cubes in all	Left in the frame	Removed
(a)	3 × 3 × 3	27	8 corners + 12 × 1 = 20	27 − 20 = 7
(b)	4 × 4 × 4	64	8 corners + 12 × 2 = 32	64 − 32 = 32
(c)	5 × 5 × 5	125	8 corners + 12 × 3 = 44	125 − 44 = 81

Check it a second way — count what was taken out

(a) middle of each face: 1 × 6 = 6, plus 1 inside → 6 + 1 = 7 ✓
(b) middle of each face: 4 × 6 = 24, plus 2 × 2 × 2 = 8 inside → 24 + 8 = 32 ✓
(c) middle of each face: 9 × 6 = 54, plus 3 × 3 × 3 = 27 inside → 54 + 27 = 81 ✓

Each hole goes right through, so the cubes inside the big cube come out as well.

Why the edge cubes stay: A frame is only the skeleton — the 8 corners and the 12 edges joining them. On a cube of side n, each edge keeps (n − 2) cubes between its two corners. So the frame always holds 8 + 12 × (n − 2) small cubes.

Look at how fast it grows: 7, then 32, then 81 cubes removed. The bigger the cube, the more of it is hidden inside — and the inside is exactly the part that gets thrown away.

Q3.

Nisha has glued 27 small cubes together to make a large solid cube. She paints the large cube red. How many of the original small cubes have — (a) three faces painted red? (b) two faces painted red? (c) one face painted red? (d) no faces painted red?

Answer

(a) 8 (b) 12 (c) 6 (d) 1

27 small cubes make a big cube that is 3 across, 3 deep and 3 tall, because 3 × 3 × 3 = 27. Nisha paints only the outside. So how much paint a small cube gets depends on where it sits.

Where the small cube sits	How many faces are painted	How many such cubes
At a corner of the big cube	3	8 (a cube has 8 corners)
In the middle of an edge	2	12 (a cube has 12 edges, 1 cube on each)
In the middle of a face	1	6 (a cube has 6 faces, 1 cube on each)
Right in the centre, hidden inside	0	1

Check the total:
8 + 12 + 6 + 1 = 27 ✓
Every small cube has been counted exactly once.

The middle layer has 4 edge cubes, 4 face-middle cubes and the hidden centre cube.

Why the centre cube gets no paint: It is completely surrounded — a cube above it, one below, and one on each of its four sides. The brush can never reach it. Break the big cube open and you would find one plain white cube in the middle.

Try a bigger one: If Nisha had used 64 small cubes (4 × 4 × 4), the answers would be 8 corners, 24 edge cubes, 24 face-middle cubes and 8 hidden ones. Check: 8 + 24 + 24 + 8 = 64 ✓

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