A 4 cm cube is to be cut into 1 cm cubes. What will be the total surface area of all the small cubes?

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382 c m 2

384 c m 2 .

385 c m 2

380 c m 2

answer is B.

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Detailed Solution

Given that,
Length of the cube = 4 cm
Length of the smaller cube = 1 cm
The volume of a cube with a length of 4cm,

= a 13

...........(1)
Substituting the value

a 1 = 4

in equation (1),
The volume of 4cm cube

= 43 c m 3

4 × 4 × 4 cm 3

= 64 c m 3

............(2)
The volume of cube with length 1cm,

= a 23

...............(3)
Substituting the value

a 2 = 1

in equation (2),
The volume of cube=

1 ³ cm ³

.
= 1 cm³...............(4)
Dividing equation (2) by (4) to get the number of small cubes formed.
=

64 cm 3 1 cm 3

The number of smaller cubes formed= 64.............(5)
The total surface area of one small cube= 6a²..............(6)
Substituting the value a=1 in equation (6).
Total surface area,
=

6 × 1 × 1cm ²

6 cm ²

...............(7)
Multiplying equation (5) with (7) to get the total surface area of small cubes formed. The total surface area of the smaller cubes formed=