Question

A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height. Two sides measuring 5 cm
x 4 cm are coloured in red. Two faces measuring 4 cm x 3 cm are coloured in blue. Two faces measuring 5
cm x 3 cm are coloured in green. Now the block is divided into small cubes of side 1 cm each. How many
small cubes will have will have three faces coloured ?
Select one:
O a. 14
O b. 10
O c. 12
O d. 8​

Answer 1

Answer:

D = 8

The answer option D

8

Answer 2

Option D : 8 cubes in the cuboid corner will have three faces of it painted.

Given :

Length of the cuboid = 4 cm

Breadth of the cuboid = 3 cm

Height of the cuboid = 5 cm

To Find :

The number of small cubes with three faces colored

Solution :

The cuboid is painted in the given conditions :

• The 2 faces with dimensions 4 X 5 are colored Red
• The 2 faces with dimensions 4 X 3 are colored Blue
• The 2 faces with dimensions 3 X 5 are colored Green

After the painting, the cuboid is divided into small cubes of dimensions 1cm.

The length, breadth, and height of the cuboid edges will have 4, 3, and 5 cubes along them respectively.

The number of small cubes formed = $3 * 4 * 5$

                                                           $= 60$

The small cubes will have paints as :

1. The corner cubes are in contact with 3 faces of the cuboid and thus will have 3 sides painted
2. The edges cubes are in contact with 2 faces side by side and thus will have 2 sides painted
3. The cubes on the cuboid face will have 1 side painted
4. The cubes inside the cuboid are not in contact with any face and thus will have 0 sides painted

Thus, number of cubes with 3 sides painted

             = Number of cubes in the corner of the cuboid

             = 8 ( each corner of cuboid will form one corner cube )

Hence, 8 cubes will have the 3 sides colored.

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