40. A cube of side 3 units is formed using a set of
smaller cubes of side 1 unit; Find the
proportion of the number of faces of the
smaller cubes visible to those which are NOT
visible.
(GATE-15)
(a) 1:4 (6) 1:3 (c) 1:2 (d) 2:3
Answers
the answer would be 1:3
Answer:
The proportion of the number of faces of the smaller cubes visible to those which are NOT visible is 1:2
Step-by-step explanation:
Volume of a cube =side ³
Volume of a cube with side 3 units= 3³=27 unit³
Volume of a cube with side 1 unit=1³=1 unit³
Number of smaller cube used = volume of larger cube ÷ volume of smaller cubes
∴Number of smaller cube used =27÷1 = 27
A cube has 6 faces
total number of faces for all smaller cubes= 6*27 =162
number of faces of smaller cubes on larger cube = 9
total number of visible faces of smaller cubes on larger cube = 9*6 =54
total number of not visible faces of smaller cubes on larger cube =
=162 - 54
=108
the
proportion of the number of faces of the smaller cubes visible to those which are NOT visible = 54 : 108 = 1:2