Cube & Cuboid

National Talent Search Examination or NTSE mental ability test subject Cube & Cuboid sample paper with answer key for 2020 exam.

Chapter – Cube & Cuboid (MAT)

Direction : Each of the following questions from 1 to 5 is based on the following information -
(i)     A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
(ii)    Two faces measuring 4 cm × 1 cm are coloured in black.
(iii)   Two faces measuring 6 cm× 1 cm are coloured in green.
(v)    The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm (from 4 cm side).

Q1.

How many cubes having red, green and black colours on at lest one side of the cube will be formed –
        (A) 16                            (B) 12                           (C) 10 (D) 8        (E) none of these.

Q2.

How many small cubes will be formed ?
        (A) 6                              (B) 12                           (C) 16 (D) 24

Q3.

How many cubes will remain if the cubes having black and green coloured are removed ?
        (A) 4                              (B) 8                             (C) 12 (D) 16        (E) none of these.

Q4.

How many cubes will have green coloured on two sides and rest of the four sides having no colour ?
        (A) 12                            (B) 10                           (C) 8 (D)4        (E) none of these.  

Q5.

How many cubes will have 4 coloured sides and two non-coloured sides ?
        (A) 8                              (B) 4                             (C) 16 (D) 10        (E) None of these.

Direction – Each of the questions from 6 to 9 is based on the following information –
(i)   There is a cuboid whose dimensions are 4×3×3 cm.
(ii)  The opposite faces of dimensions 4 ×3 are coloure yellow.
(iii) The opposite faces of other dimensions 4 ×3 are coloured red.
(iv) Now the cuboid is cut into small cubes of side 1 cm.

Q6.

How many small cubes will have only one face coloured ?
        (A) 10                            (B) 12                           (C) 14 (D) 18        (E) none of these.

Q7.

How many small cubes will have only two faces coloured ?
        (A) 12                            (B) 24                           (C) 16 (D) 12        (E) None of these.

Q8.

How many small cubes will have no face coloureod?
        (A) 1                              (B) 2                             (C) 4 (D) 8        (E) None of these.

Q9.

How many small cubes have three faces coloured ?
        (A) 24                            (B) 20                           (C) 16 (D) 12

Direction – Each of the questions from 10 to 13 is based on the following informations -
(i)   A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
(ii)  Two sides measuring 5cm×4cm are coloured in red.
(iii) Two sides measuring 4cm×3cm are coloured in blue.
(iv) Two sides measuring 5cm×3cm are coloured in green.
(v)  Now the block is divided into small cubes of side 1 cm each.

Q10.

How many small cubes will have only one face coloured ?
        (A) 12                            (B) 28 (C) 22                 (D) 16        (E) None of these.

Q11.

How many small cubes will have three faces coloured ?
        (A) 14                            (B) 8                             (C) 10 (D) 12        (E) None of these.

Q12.

How many small cubes will have no faces colourd ?
        (A) 0                              (B) 2                             (C) 4 (D) 6        (E) none of these.

Q13.

How many small cubes will have two faces coloured with red and green colours ?
        (A) 12                            (B) 8                             (C) 16 (D) 20        (E) None of these.

Direction- Each of the questions from 14 to 17 is based on the following informations -
(i)   All the faces of cubes are painted with red colour.
(ii) The cubes is cut into 64 equal small cubes.

Q14.

How many small cubes have no faces coloured ?
        (A) 24                            (B) 8                             (C) 16 (D) 0

Q15.

How many small cubes have no faces coloured ?
        (A) 24                            (B) 8                             (C) 16 (D) 0

Q16.

How many such small cubes are there whose two adjacent faces are coloured red ?
        (A) 0                              (B) 8                             (C) 16 (D) 24

Q17.

How many small cubes are there whose three faces are colourd ?
        (A) 4                              (B) 8                             (C) 16 (D) 24

Q18.

A cube has been painted red, yellow and green on pairs of opposite faces. The cube is then cut into 64 small cubes. How many small cubes are whose only one face is coloured red ?
        (A) 24                            (B) 8                             (C) 16 (D) 12

Directions – Each of the questions from 19 to 23 is based on the following informations –
All the opposite faces of a big cube are coloured with red, black and green colours. After this it is cut into 64 small equal cubes.

Q19.

How many such small cubes are there whose no faces are coloured ?
        (A) 0                              (B) 4                             (C) 8 (D) 16

Q20.

How many small cubes are there whose at the most two faces are coloured ?
        (A) 48                            (B) 8                             (C) 28 (D) 24

Q21.

How many small cubes are there whose 3 faces are coloured ?
        (A) 4                              (B) 8                             (C) 16 (D) 24

Q22.

How many small cubes are there where one face is green and other one is either black or red ?
        (A) 28                            (B) 8                             (C) 16 (D) 24

Q23.

How many small cubes are there where one face is green and other one is either black or red ?
        (A) 18                            (B) 8                             (C) 16 (D) None of these

Direction – All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.

Q24.

How many small cubes will be formed having no face coloured ?
        (A) 27                            (B) 8                             (C) 16 (D) 24        (E) 32

Q25.

How many small cubes will be formed having only one face coloured ?
        (A) 54                            (B) 8                             (C) 16 (D) 24        (E) 36

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