Question

8. 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

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

Answer 2

cube side =12cm

volume of cube =side³

=12³

=12×12×12

= 1728

volume of new cube which is cut into 8cubes of equal volume from old cube

=1728/8

=216

volume =side³

side³=216

side = ³√(216)

side = 6cm(new cube)

surface area of cube= 6×side2

SA of old cube/surface area of new cube

=(6×12²)/(6×6²)

=(12×12)/(6×6)

=2×2/1

=4/1

ratio of old to new cube = 4:1