Question

A cuboid of dimensions (6 cm$\times$4 cm$\times$1 cm) is painted black on both the surfaces of dimensions (4 cm$\times$1 cm), green on the surfaces of dimensions (6 cm $\times$ 4 cm) and red on the surfaces of dimensions (6 cm$\times$1 cm). Now the block is divided into various smaller cubes of side 1 cm each. The smaller cubes so obtained are separated.

How many cubes will have all three colours black, green and red each at least on one side?

• A. 16
• B. 12
• C. 10
• D. 8

Answer 1

The correct option is A 16

Number of smaller cubes having all three colours black, green and red
each atleast on one side = Number of smaller cubes at $4$ corners +
Number of smaller cubes at the $2$ edges of surfaces of dimensions
$(4cm\times 1cm)$ + Number of smaller cubes at the $2$ edges of
surfaces of dimensions $(6cm\times 1cm)$
$=4+2+2+4+4=4+4+8=16$