Question

a solid cube 12 cm is cut........guys plzz explain it need help today is my exxam

Answer 1

hey !!!

volume of big cube

= a³ =12³ = 1728

let the side of new cube which seperated out from big cube be x cm

volume of new cube separated out from big cube =x³

now...no. of small cube =volume of big cube /volume of small cube

=> 8 =1728/x³

x =3√1728/8 = 12/2 =6cm..

now ...surface area of big cube =6 ×a² =6 ×12²

=> 6×144 =>. 864cm²---------1)

and surface area of small cube

=> 6×6² =216--------2)

now dividing 1 to 2 we get ...

ratio of surface area = 864/216 =4/1

4:1 Answer ...

hope it helps you !!!

$Rajukumar111

Answer 2

hiii!!!

here's ur answer...

given the side of the big cube is 12cm.

volume of the cube = side³

= 12 × 12 × 12

= 1728cm³

according to the question we have to find the side of the cube after cutting the big cube into 8 equal measure of cubes. so first we have to find the volume of each small cube.

volume of the small cube = 1728/8

= 216cm³

therefore side³ = 216cm³

==> side = ³√216

==> side = 6cm

VERIFICATION:-

volume of the cube ( side = 6cm ) = side³

= 6 × 6 × 6

= 216cm³

hence verified

thus the side of the small cube is 6cm.

now,

TSA (surface area) of the big cube = 6 × side²

= 6 × 12²

= 6 × 144

= 864cm²

TSA of the small cube = 6 × side²

= 6 × 6²

= 6 × 36

= 216cm²

ratio between their surface areas :-

=> ( 864 : 216 ) ÷ 2

=> ( 432 : 108 ) ÷ 2

=> ( 216 : 54 ) ÷ 2

=> ( 108 : 27 ) ÷ 3

=> ( 36 : 9 ) ÷ 3

=> ( 12 : 3 ) ÷ 3

=> 4 : 1

final answer is 4 : 1

hope this helps u..!!