Question

A solid cube of side 14cm is cut into 64 cubes of equal volume. what will be the side of the new cube . also find the ratio between their surface area.

Answer 1

Let S be side of original cube & s be the side of smaller cube.

V be the volume of bigger cube & v be the volume of the smaller cube.
Since bigger cube is divided in 64 pieces of equal volume,
V=64v
S³=64s³
14³=64s³
s³=14³/64=2744/64=42.875
$s = \sqrt[3 ]{42.875}$
s=3.5cm

Surface area of bigger cube = 6*area of each face
A=6*S²
Similarly surface area of smaller cube = a=6*s²
Ratio of surface areas=A/a
R=6S²/6s²=S²/s²=14²/3.5²=196/12.25=16/1

Side of smaller cube = s = 3.5cm
Ratio of surface areas = A:a = 16:1