Question

A solid cube of side 12 cm is cut into 8 cubes of equal volumes.what will be the side of the new cube?also find the ratio between their surface areas

Answer 1

Given :

• Side of cube = 12 cm

• No. of cubes = 8

To Find :

• Number of cubes formed when given cube cutted into 8 cubes of equal volume

• Ration between Area of given cube and new cube

Solution :

Volume of Cube = a³

→ Vol = 12 × 12 × 12

→ Vol = 1728 cm³

Now this cube is cutted into 8 equal cubes.

→ 1728 / 8

→ 216 cm³

Vol of new cube is 216 cm³. Now we have to find side of this cube

→ a'³ = 216

→ a' = 6 cm

Side of new cube is 6 cm

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Ratio of Area

6a² : 6a'² = a² : a'²

→ ( 12 )² : ( 6 )²

→ 144 : 36

→ 4 : 1

Answer 2

Given:-

• A solid cube of side 12 cm is cut into 8 cubes of equal volumes.

To find:-

• Side of new cube
• Ratio b/w their surface areas

Solution:-

Let's the side of solid cube = a cm

Let's the side of new cube = a' cm

Therefore,

Volume of larger cube = (a)³

= (12)³

= 12 × 12 × 12

= 1728 cm³

Eight small cubes of equal volume are cut from the larger one.

→ Volume of large cube = 8 × Volume of one new cube

→ 1728 = 8 × (a')³

→ 1728/8 = (a')³

→ 216 = (a')³

★ Volume of one new cube = 216cm³

★ Then, side of new cube (a') = ∛216 = 6cm

Therefore, The ratio of surface area of larger cube and the smaller cube :-

→ Surface of larger cube / Surface area of smaller cube

→ 6(a)²/ 6(a')²

→ 6 × 12²/ 6 × 6²

→ 864/216

→ 4/1

Hence, The ratio of surface area of larger cube and the smaller cube is 4:1

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