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Test: Cubes & Cuboids - 1 - CAT MCQ


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15 Questions MCQ Test - Test: Cubes & Cuboids - 1

Test: Cubes & Cuboids - 1 for CAT 2024 is part of CAT preparation. The Test: Cubes & Cuboids - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test: Cubes & Cuboids - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes & Cuboids - 1 below.
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Test: Cubes & Cuboids - 1 - Question 1
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. 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).

Question -

How many cubes having red, green and black colours on at least one side of the cube will be formed ?

Detailed Solution for Test: Cubes & Cuboids - 1 - Question 1

Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.

Hence, the number of such small cubes is 4.

Test: Cubes & Cuboids - 1 - Question 2
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. 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).

Question -

How many small cubes will be formed ?

Detailed Solution for Test: Cubes & Cuboids - 1 - Question 2

Number of small cubes = l x b x h = 6 x 4 x 1 = 24

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Test: Cubes & Cuboids - 1 - Question 3
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. 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).

Question -

How many cubes will have 4 coloured sides and two non-coloured sides ?

Detailed Solution for Test: Cubes & Cuboids - 1 - Question 3

Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 non-coloured sides.

Test: Cubes & Cuboids - 1 - Question 4
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. 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).

Question -

How many cubes will remain if the cubes having black and green coloured are removed ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 4

Number of small cubes which are Black and Green is 8 in all.

Hence, the number of remaining cubes are = 24 - 8 = 16

Test: Cubes & Cuboids - 1 - Question 5
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. 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).

Question -

How many cubes will have green colour on two sides and rest of the four sides having no colour ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 5

There are 16 small cubes attached to the outer walls of the cuboid.

Therefore remaining inner small cubes will be the cubes having two sides green coloured.

So the required number = 24 - 16 = 8

Test: Cubes & Cuboids - 1 - Question 6
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Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have only two faces coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 6

Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right

= 16

Test: Cubes & Cuboids - 1 - Question 7
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Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes have three faces coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 7

Such cubes are related to the corners of the cuboid and there are 8 corners.

Hence, the required number is 8.

Test: Cubes & Cuboids - 1 - Question 8
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Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have no face coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 8

Number of small cubes have no face coloured = (4 - 2) x (3 - 2) = 2 x 1 = 2

Test: Cubes & Cuboids - 1 - Question 9
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Directions to Solve

The following questions are based on the information given below:

  1. There is a cuboid whose dimensions are 4 x 3 x 3 cm.
  2. The opposite faces of dimensions 4 x 3 are coloured yellow.
  3. The opposite faces of other dimensions 4 x 3 are coloured red.
  4. The opposite faces of dimensions 3 x 3 are coloured green.
  5. Now the cuboid is cut into small cubes of side 1 cm.

Question -

How many small cubes will have only one face coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 9

Number of small cubes having only one face coloured = 2 x 2 + 2 x 2 + 2 x 1

= 4 + 4 + 2

= 10

Test: Cubes & Cuboids - 1 - Question 10
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
  2. Two sides measuring 5 cm x 4 cm are coloured in red.
  3. Two faces measuring 4 cm x 3 cm are coloured in blue.
  4. Two faces measuring 5 cm x 3 cm are coloured in green.
  5. Now the block is divided into small cubes of side 1 cm each.

Question -

How many small cubes will have will have three faces coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 10

Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners.

Hence, the required number of small cubes is 8.

Test: Cubes & Cuboids - 1 - Question 11
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
  2. Two sides measuring 5 cm x 4 cm are coloured in red.
  3. Two faces measuring 4 cm x 3 cm are coloured in blue.
  4. Two faces measuring 5 cm x 3 cm are coloured in green.
  5. Now the block is divided into small cubes of side 1 cm each.

Question -

How many small cubes will have only one face coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 11

2 from the front + 2 from the back + 3 from the left + 3 from the right + 6 from the top + 6 from the bottom = 22

Test: Cubes & Cuboids - 1 - Question 12
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
  2. Two sides measuring 5 cm x 4 cm are coloured in red.
  3. Two faces measuring 4 cm x 3 cm are coloured in blue.
  4. Two faces measuring 5 cm x 3 cm are coloured in green.
  5. Now the block is divided into small cubes of side 1 cm each.

Question -

How many small cubes will have no faces coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 12

Required number of small cubes = (5 - 2) x (4 - 2) x (3 - 2)

= 3 x 2 x 1

= 6

Test: Cubes & Cuboids - 1 - Question 13
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Directions to Solve

The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
  2. Two sides measuring 5 cm x 4 cm are coloured in red.
  3. Two faces measuring 4 cm x 3 cm are coloured in blue.
  4. Two faces measuring 5 cm x 3 cm are coloured in green.
  5. Now the block is divided into small cubes of side 1 cm each.

Question -

How many small cubes will have two faces coloured with red and green colours ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 13

Required number of small cubes = 6 from the top and 6 from the bottom = 12

Test: Cubes & Cuboids - 1 - Question 14
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Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes have only one face coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 14

Number of small cubes having only one face coloured = (x - 2)2 x No. of faces

= (4 - 2)2 x 6

= 24

Test: Cubes & Cuboids - 1 - Question 15
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Directions to Solve

The following questions are based on the information given below:

  1. All the faces of cubes are painted with red colour.
  2. The cubes is cut into 64 equal small cubes.

Question -

How many small cubes have no faces coloured ?
Detailed Solution for Test: Cubes & Cuboids - 1 - Question 15

Number of small cubes having only one faces coloured = (x - 2)3

Here, x = side of big cube / side of small cube

x = 4 /1

x = 4

Required number = (4 -2)3

= 8

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