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Test: Cubes and Dice- 1 - Class 10 MCQ


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10 Questions MCQ Test Olympiad Preparation for Class 10 - Test: Cubes and Dice- 1

Test: Cubes and Dice- 1 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The Test: Cubes and Dice- 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Cubes and Dice- 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes and Dice- 1 below.
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Test: Cubes and Dice- 1 - Question 1

A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.

How many cubes have at least one face coloured pink?

Detailed Solution for Test: Cubes and Dice- 1 - Question 1

If the cube is cut into 125 smaller cubes, how are the cuts made? 4 cuts/slices in x, y, z– planes respectively. So the cube is a 5 × 5 × 5 cube. That is, it has 5 squares on each of its faces.
So if only one face is painted pink, how many cubes have at least 1 face colored in pink? It is the number of cubes with only one side colored in pink because pink is only colored on one face. So, the answer would be: 5 ∗ 5=25

Test: Cubes and Dice- 1 - Question 2

A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.

How many cubes have at least two faces coloured?

Detailed Solution for Test: Cubes and Dice- 1 - Question 2

There will be at least two faces coloured on 21 cubes.

Test: Cubes and Dice- 1 - Question 3

A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.

How many cubes are coloured silver on one face, orange or pink on another face and have four uncoloured faces?

Detailed Solution for Test: Cubes and Dice- 1 - Question 3

Only one face colored.

Test: Cubes and Dice- 1 - Question 4

A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. Now the cube is cut into sixty four smaller cubes of equal size.

How many smaller cubes will have no surface painted?

Test: Cubes and Dice- 1 - Question 5

A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. Now the cube is cut into sixty four smaller cubes of equal size.

How many smaller cubes have three surfaces painted?

Test: Cubes and Dice- 1 - Question 6

A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. Now the cube is cut into sixty four smaller cubes of equal size.

How many smaller cubes have at least one surface painted with green colour?

Test: Cubes and Dice- 1 - Question 7

A cube of 4 cm has been painted on its surfaces in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. Two remaining surfaces are unpainted. Now the cube is cut into smaller cubes of side 1 cm each.

How many cubes will have at least red colour on its surfaces?

Test: Cubes and Dice- 1 - Question 8

A cube of 4 cm has been painted on its surfaces in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. Two remaining surfaces are unpainted. Now the cube is cut into smaller cubes of side 1 cm each.

How many cubes will have only two surfaces painted with red and blue colour respectively?

Test: Cubes and Dice- 1 - Question 9

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

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 and Dice- 1 - Question 9


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 and Dice- 1 - Question 10

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

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

Detailed Solution for Test: Cubes and Dice- 1 - Question 10


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

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