Question

A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be
the side of the new cube? Also, find the ratio between their surface areas.​

Answer 1

Step-by-step explanation:

i hope this will help you !

Answer 2

Given :-

A solid cube of side 12 cm is cut into eight cubes of equal volume.

To Find :-

The side of the new cube.

The ratio between their surface areas.​

Solution :-

We know that,

• s = Side
• a = Area

By the formula,

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

Given that,

Side of a cube = 12 cm

Substituting their values,

Volume of cube = (12)³

Volume = 1728 cm³

Surface area of a cube with side 12 cm = 6a²

Surface area = 6(12)²    ....(1)

Given that,

Cube is cut into eight small cubes of equal volume.

Let the side be 's'.

Volume of a small cube = s³

Surface area = 6s²    ....(2)

Volume of each small cube = Volume of cube ÷ 8

Substituting their values,

$\sf Volume=\dfrac{1728}{8} =216 \ cm^{3}$

Side = 216 cm³

Side = 6 cm

$\sf Surface \ areas \ of \ cubes \ ratios=\dfrac{Surface \ area \ of \ bigger \ cube }{ Surface \ area \ of \ smaller \ cubes }$

From equation (1) and (2),

Surface areas of the cubes ratios,

$\sf \dfrac{6a^{2}}{6s^{2}} =\dfrac{a^{2}}{s^{2}} =\dfrac{12^{2}}{6^{2}} =4$

Therefore, the ratio between their surface area is 4 : 1.