Question

a 4 cm cube is cut into 1 cm cubes. calculate the total surface area of all the small cubes.​

Answer 1

Answer:

$\bigstar{\bold{TSA\:of\:64\:cubes=384\:cm^{2} }}$

Step-by-step explanation:

$\Large{\underline{\bf{Given:}}}$

• 4 cm cube is cut into 1 cm cubes

$\Large{\underline{\bf{To\:Find:}}}$

• The total surface area of all the cubes

$\Large{\underline{\bf{Solution:}}}$

⇝ First we have to find the number of small cubes formed.

⇝ For that we have to find the volume of both the cubes.

⇝ Volume of a cube is given by,

    Volume of a cube = a³

    where a is a side of the cube.

⇝ Hence,

    Volume of bigger cube = 4³

    Volume of bigger cube = 64 cm³

⇝ Volume of  smaller cube = 1³ = 1 cm³

⇝ Now,

    Number of cubes = Volume of bigger cube/Volume of smaller cube

    Number of cubes = 64/1

    Number of cubes =  64

⇝ Now we have to find the total surface area of one cube.

⇝ Total surface area of a cube is given by,

    TSA of cube = 6a²

⇝ Substitute the data,

    TSA of a cube = 6 × 1²

    TSA of the cube = 6 cm²

⇝ Now the TSA of 64 cubes is given by

    TSA of 64 cubes = 6 × 64

    TSA of 64 cubes = 384 cm²

    $\boxed{\bold{TSA\:of\:64\:cubes=384\:cm^{2} }}$

Answer 2

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Volume of 4 cm^3 = (4)^3cm^3 = 64cm^3

Volume of 1 cm^3 = (1)^3cm^3 = 1 cm^3

Total no. of 1 cm cubes = Volume of 4 cm^3 / Volume of 1 cm^3

=> 64/1

=> 64

Surface Area of 1 cube = 6(side)^2 cm^2

Surface Area of 1 cube = 6(1)^2 cm^2

Surface Area of 1 cube = 6 cm^2

TSA of all small cubes = 64 × 6 cm^2

=> 384 cm^2