Question

A cuboid of dimensions (12cm × 8cm × 2 cm) is painted black on both the surfaces of dimensions (8cm × 2 cm), green on the surfaces of dimensions (12cm × 8cm) and red on the surfaces of dimensions (12cm × 2 cm). Now the block is divided into various smaller cubes of side 2cm each. The smaller cubes so obtained are separated. How many cubes will have atleast three surfaces coloured? (1) 16 (2) 12 (3) 10 (4) 8
answer is 16 but how???​

Answer 1

Step-by-step explanation:

Number of cubes formed = (12 * 8 * 2)/(2 * 2 * 2) = 24 cubes . Since, a cuboid has 8 corners and we know that, cube whose three surfaces are coloured are on the corners only . Therefore, we can conclude that, the cubes with atleast three surfaces coloured are 3 only.

Answer 2

Dimensions of cuboid = (12cm×8 cm×2cm)

Painted black on both surfaces of dimensions = (8 cm×2cm).

Painted green on both surfaces of dimensions (12cm×8cm)

Painted red on both surfaces of dimensions (12cm×2cm)

now, given that, the block is divided into various smaller cubes of side 2cm each.

so,

Number of cubes formed = (12×8×2)/(2×2×2) = 24 cubes.

Since, a cuboid has 8 corners and we know that, cube whose three surfaces are coloured are on the corners only.

Therefore, we can conclude that, the cubes with atleast three surfaces coloured are 3 only.