Question

A solid cube of side 12cm is cut into 8 cubes of equal volume what will be the side of the new cube also find the ratio between their surface areas.
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Answer 1

Answer:

Side is 6cm, 4:1

Step-by-step explanation:

For obtaing 8 cubes we have to cut it from half from all sides

i.e 6cm

So,

Surface area= 6a^2

For 12cm cube

= 6*12^2

= 6*144

And for 6cm cube

= 6*6^2

= 6*36

So, the ratio is

6*144/6*36

= 4:1

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Answer 2

SOLUTION:-

Given:-

• Edge of a solid cube = 12cm
• No. of cubes that is needed to be cut = 8

Need to find:-

• The side of the new cube.
• The ratio between their surface areas.

Explaination:-

As it given that,

Edge of solid cube is 12cm

Therefore,

Volume of solid cube = a³ = 12cm³

Now,

Let the side of the new cube be x cm.

Therefore,

Volume of new cube = x³cm³

Therefore,

Volume of 8 such cubes = 8×x³cm³

According to question,

=> 8x³ = 12³

=> 8x³ = 432

=> x³ = 432/8

=> x³ = 54

=> x = 6×6×6

=> x = 6cm³

Surface area of cube of edge 12cm = 6a²

Surface area of cube = 6a³ = 6×6²cm³

Ratio of their surface areas:-

Surface area of old cube/surface area of new cube

=> 6×12×12/6×6×6

=> 4/1

=> 4:1