Question

7. A 4cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes
​

Answer 1

Answer:

384 cm

Step-by-step explanation:

Vol. of 4cm cube =(4)

=64cm

Vol. of 1cm cube =(1)

Total no. of 1cm cubes =

Vol. of 1 cm cube

Vol.of 4 cm cube

=

1

64

=64

Surface area of 1 cube =6(side)

Surface area of 1 cube =6(1)

Surface area of 1 cube =6cm

Total surface area of all small cubes =64×6cm

=384cm

Answer 2

Given :-

A 4 cm cube is cut into 1 cm cubes.

To Find :-

The total surface area of all the small cubes.

Analysis :-

Consider the number of cubes as a variable.

Substitute the values in the formula of volume of cube accordingly.

Then find the TSA accordingly.

Solution :-

We know that,

• s = Side
• TSA = Total Surface Area

Let the number cubes be 'x'.

Volume of big cube = x (Volume of small cube)

By the formula,

$\underline{\boxed{\sf Volume \ of \ cube=Side^3}}$

Let the side be 's'.

Substituting their values,

$\sf s^3=x(s^3)$

$\sf 4^3=x(1)^3$

$\sf 64=x$

By the formula,

$\underline{\boxed{\sf Total \ surface \ area \ of \ cube=6(Side)^2}}$

Substituting them,

TSA = 6 × 1²

TSA = 6 cm²

Therefore,

TSA of 64 cubes = 6 × 64

TSA = 384 cm²

Therefore, the total surface area of all the small cubes is 384 cm².