Question

2) A solid cube of side 12 cm is cut into 8 identical cubes each having
the same volume. What will be the side of the new cubes? Also find
out the surface area of both the cubes?​

Answer 1

Volume Of New Cubes is 216 cm²

Surface Area Of Original Cube is 864 cm²

Surface Area Of New Cubes is 216 cm²

Step-by-step explanation:

GIVEN

Side = 12 cm

Identical Cube = 8 of equal Sides

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TO FIND

Volume Of New cubes

Surface Area Of Original Cube

Surface Area Of New Cubes

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Volume Of Original Cubes

We know that,

Volume Of Cube = Side³

Volume Of Cube = 12³

Volume Of Cube = 1728

Volume Of Cube = 1728 cm²

Volume Of Original Cube is 1728 cm²

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Volume Of New Cubes

Volume Of New Cubes = Volume Of Original Cube / 8

Volume Of New Cubes = 1728 / 8

Volume Of New Cubes = 216

Volume Of New Cubes = 216 cm²

Volume Of New Cubes is 216 cm²

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Side Of New Cubes

We know that,

Volume Of Cube = Side³

216 = Side³

Side = ∛216

Side = 6

Side = 6 cm

Side of new cubes is 6 cm

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Surface Area Of Original Cube

We know that,

Surface Area Of Cube = 6 × Side²

Surface Area Of Cube = 6 × 12²

Surface Area Of Cube = 6 × 144

Surface Area Of Cube = 864

Surface Area Of Cube = 864 cm²

Surface Area Of Original Cube is 864 cm²

___________________________

Surface Area Of New Cubes

We know that,

Surface Area Of Cube = 6 × Side²

Surface Area Of Cube = 6 × 6²

Surface Area Of Cube = 6 × 36

Surface Area Of Cube = 216

Surface Area Of Cube = 216 cm²

Surface Area Of New Cubes is 216 cm²