Question

a cube of side 12cm is cut into eight smaller cubes of the same volume. find the ratio of the surface areavof the old cube to the new cube​

Answer 1

Answer:

Side of a large cube(a) = 12cm

volume of the cube = (12³)cm³

=> 1728 cm³

eight small cubes of equal volumes are cut from the larger one  

∴volume of larger cube = 8* volume of one small cube.

=>1728 = 8 * volume of small cube

=>1728/8 = volume of small cube

∴volume of one small cube = 216.

then side of the smaller cube = ∛216 = 6cm

The ratio of surface area of larger cube  and small cube = 864:216 = 4:1

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Answer 2

Answer:

Given:

Side 12cm

⇒Volume of cube =12×12×12=1728cm

3

⇒Volume of smaller cube

=

8

1

of 1728

=

8

1

×1728=216cm

3

⇒Let side be S.

∴ (S)

3

=216

⇒S=6 cm

Ratio of SA of cubes

=

SA of smaller cube

SA of bigger cube

=(

6

12

)

2

=

1

2

2

=

1

4

∴ Ratio between their surface areas 4:1

Answered By

toppr

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