A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 c...........

Logical Resoning (CGL) Cubes and Dice

A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of

smaller cubes having only one face painted.

This questions was previously asked in

SSC CGL 13th April 2022 Shift-2

150

100

- A large cube has a side of 49 cm. It's divided into smaller cubes with sides of 7 cm.

- To find the number of smaller cubes, divide each dimension of the large cube by 7: \( \frac{49}{7} = 7 \).

- The large cube becomes a \( 7 \times 7 \times 7 \) grid of smaller cubes, totaling 343 smaller cubes.

- Smaller cubes with only one face painted are those on the faces but not on the edges or corners.

- Each face of the cube has \( (7-2) \times (7-2) = 5 \times 5 = 25 \) such cubes.

- There are 6 faces, so total cubes with one face painted are \( 6 \times 25 = 150 \).

Therefore, Option 2: 150 is the correct answer.

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