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The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured?
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The outer border of width 1cm of a cube with side 5 cm is painted yell...
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The outer border of width 1cm of a cube with side 5 cm is painted yell...
Solution:
Given: Side of the cube = 5 cm
Width of the outer border = 1 cm
Number of smaller cubes = 125
Side of each smaller cube = 1 cm
To find: How many smaller cubes have at least one face coloured?
Explanation:
Step 1: Calculate the side of the cube including the outer border.
Side of the cube including the outer border = 5 cm + 2(1 cm)
= 7 cm
Step 2: Calculate the number of smaller cubes that can be formed.
As each side of the cube is 7 cm, it can be divided into 7 smaller cubes of 1 cm each.
So, the total number of smaller cubes that can be formed = 7 x 7 x 7
= 343
Step 3: Calculate the number of smaller cubes which are completely painted yellow on all sides.
As the outer border is painted yellow on all sides, the total number of smaller cubes that are completely painted yellow on all sides = 5 x 5 x 5
= 125
Step 4: Calculate the number of smaller cubes which are completely unpainted.
As the outer border is 1 cm wide, the smaller cubes that are formed at the corners of the cube will have no face painted.
So, the total number of smaller cubes which are completely unpainted = 8
Step 5: Calculate the number of smaller cubes which have at least one face coloured.
To calculate this, we need to subtract the number of completely unpainted cubes from the total number of smaller cubes.
Number of smaller cubes which have at least one face coloured = Total number of smaller cubes - Number of completely unpainted cubes
= 343 - 8
= 335
Therefore, there are 335 smaller cubes which have at least one face coloured.
Summary:
The given cube with a side of 5 cm and an outer border of 1 cm was divided into 125 smaller cubes of 1 cm each. Out of these, 125 smaller cubes were completely painted yellow, 8 were completely unpainted, and 335 smaller cubes had at least one face coloured.
Given: Side of the cube = 5 cm
Width of the outer border = 1 cm
Number of smaller cubes = 125
Side of each smaller cube = 1 cm
To find: How many smaller cubes have at least one face coloured?
Explanation:
Step 1: Calculate the side of the cube including the outer border.
Side of the cube including the outer border = 5 cm + 2(1 cm)
= 7 cm
Step 2: Calculate the number of smaller cubes that can be formed.
As each side of the cube is 7 cm, it can be divided into 7 smaller cubes of 1 cm each.
So, the total number of smaller cubes that can be formed = 7 x 7 x 7
= 343
Step 3: Calculate the number of smaller cubes which are completely painted yellow on all sides.
As the outer border is painted yellow on all sides, the total number of smaller cubes that are completely painted yellow on all sides = 5 x 5 x 5
= 125
Step 4: Calculate the number of smaller cubes which are completely unpainted.
As the outer border is 1 cm wide, the smaller cubes that are formed at the corners of the cube will have no face painted.
So, the total number of smaller cubes which are completely unpainted = 8
Step 5: Calculate the number of smaller cubes which have at least one face coloured.
To calculate this, we need to subtract the number of completely unpainted cubes from the total number of smaller cubes.
Number of smaller cubes which have at least one face coloured = Total number of smaller cubes - Number of completely unpainted cubes
= 343 - 8
= 335
Therefore, there are 335 smaller cubes which have at least one face coloured.
Summary:
The given cube with a side of 5 cm and an outer border of 1 cm was divided into 125 smaller cubes of 1 cm each. Out of these, 125 smaller cubes were completely painted yellow, 8 were completely unpainted, and 335 smaller cubes had at least one face coloured.
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The outer border of width 1cm of a cube with side 5 cm is painted yell...
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The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured?
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The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured?.
The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outer border of width 1cm of a cube with side 5 cm is painted yellow on each side and the remaining space enclosed by this 1 cm path is painted pink. This cube is now cut into 125 smaller cubes of each side 1 cm. The smaller cubes so obtained are noe seperated. How many smaller cubes have at least one face coloured?.
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