Question

A cubical wooden block of length 12 cm is cut into 8 equal cubical pieces. Find the length of edge of each piece.
( answer is 6 cm)​

Answer 1

Dear Student,

● Answer -

Length of edge of each cube is 6 cm.

◆ Explaination -

[Look at the figure for better understanding.]

When cube is cut into 8 equal pieces,

Volume of bigger cube = sum of volumes of smaller cubes

L^3 = n × l^3

12^3 = 8 × l^3

1728/8 = l^3

l^3 = 216

Taking cube root,

l = 6 cm

Hence, Length of edge of each cube is 6 cm.

Thanks dear. Hope this helps you...

Answer 2

Answer:

the length of edge of each piece is 6cm.

Step-by-step explanation:

Given,

cubical of height (l) = 12cm.

equal cubical pieces(n) = 8

cube of volume (v) =( 12)^3cm^3 [ :. v = l^3]

let the small height (l) = a cm

so the volume of small cube = a^3 cm^3

volume of the bigger = volume of the 8 small cube.

Now,

l^3 = n × l^3

(12)^3 = 8×(a) ^3

(12)^3 = (2a) ^3

12 = 2a

a = 12\2

:. a = 6cm

the length of edge of each piece is 6cm.