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CAT Exam  >  CAT Tests  >  Test: Cubes & Cuboids (February 22) - CAT MCQ

Test: Cubes & Cuboids (February 22) - CAT MCQ


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10 Questions MCQ Test - Test: Cubes & Cuboids (February 22)

Test: Cubes & Cuboids (February 22) for CAT 2024 is part of CAT preparation. The Test: Cubes & Cuboids (February 22) questions and answers have been prepared according to the CAT exam syllabus.The Test: Cubes & Cuboids (February 22) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes & Cuboids (February 22) below.
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Test: Cubes & Cuboids (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - Question 2

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

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Test: Cubes & Cuboids (February 22) - 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 (February 22) - Question 3

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

Test: Cubes & Cuboids (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - Question 8

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

Test: Cubes & Cuboids (February 22) - 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 (February 22) - 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 (February 22) - 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 (February 22) - 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.

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