Question

A cube of side 10 is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size. Answer the following questions based on this statement: 1) How many cubes have at least two green faces each?
2)How many cubes are Without any color

Answer 1

Given :- A cube of side 10 is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size. Answer the following questions based on this statement:

1) How many cubes have at least two green faces each ?

2) How many cubes are Without any color ?

Answer :-

we know that, if a cubes with sides as n , then ,

• Number of cubes with 0 side painted = (n - 2)³ .
• Number of cubes with 2 sides painted = 12(n - 2) .
• Number of cubes with 3 sides painted= 8 .

given that,

→ side of cube = 10

→ colored green with a wide of = 2 cm .

so,

→ Side of each cube = 2 cm .

then,

→ Total cubes on each side = 10/2 = 5 cubes = n .

and,

→ Total cubes so formed = (5)³ = 125 cubes .

therefore,

→ How many cubes have at least two green faces each = cubes with 3 faces green(corners) + cubes with 2 faces green = 8 + 12(n - 2) = 8 + 12(5 - 2) = 8 + 12 * 3 = 8 + 36 = 44 cubes .

and,

→ How many cubes are Without any color = (n - 2)³ = (5 - 2)³ = 3³ = 27 cubes .

Learn more :-

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Answer 2

Step-by-step explanation:

1)44 cubes have at least two green faces

2)27 cubes have no colour