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

$\bf \LARGE \it Hey \: User!!!$

given the side of the solid cube = 12cm
therefore it's volume = side³
= 12 × 12 × 12
= 1728cm³

according to the question, the cube has been cut into 8 equal cubes.

therefore volume of each cube = 1728/8
= 216cm³

we know that side³ = volume of a cube

>> side³ = 216cm³
>> side = ³√216
>> side = ³√6×6×6
>> side = 6cm

hence, the side of the new cube is 6cm.

now we have to find the ratio between the surface area of both cubes..

TSA of the cube with side 12cm = 6(12)²
= 6 × 144
= 864cm²

TSA of the cube with side 6cm = 6(6)²
= 6 × 36
= 216cm²

ratio between the surface areas of both cubes :-

>> 216 : 864
>> 1 : 4

hence, final answer is => 1 : 4

$\bf \large \it{Cheers!!!}$

Answer 2

given the side of the solid cube = 12cm

therefore it's volume = side³

= 12 × 12 × 12

= 1728cm³

according to the question, the cube has been cut into 8 equal cubes.

therefore volume of each cube = 1728/8

= 216cm³

we know that side³ = volume of a cube

>> side³ = 216cm³

>> side = ³√216

>> side = ³√6×6×6

>> side = 6cm

hence, the side of the new cube is 6cm.

now we have to find the ratio between the surface area of both cubes..

TSA of the cube with side 12cm = 6(12)²

= 6 × 144

= 864cm²

TSA of the cube with side 6cm = 6(6)²

= 6 × 36

= 216cm²

ratio between the surface areas of both cubes :-

>> 216 : 864

>> 1 : 4

hence, final answer is => 1 : 4