QUESTION NO. 11
Direction: the outer border of width 1 cm 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 now separated.
How many smaller cubes have all the surface uncoloured?
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Answer:
61 small cubes are obtained.
Step-by-step explanation:
Given:
Sides of cube (a) = 5 cm
Outer border width = painted in yellow = 1 cm
Volume of cube =
Volume of a cube with side as 5 cm =
Volume of cube that is uncoloured
=
= = 64 cubes.
Therefore, the number of small cubes obtained have at least one face coloured = (Total number of cubes – number of Uncoloured cubes)
= 125-64 = 61 cubes."
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