Question

An 8cm cube is cut into 2 cm cubes. Calculate the total surface area of all the small cubes .

Answer 1

Answer:

Solution:

Total surface area of cuboid of size 8 cm , 4 cm and 2 cm is given by the formula = 2 ×[LB+B H+H L]

Where, L=Length, B=Breadth, H=Height

=2 ×[ 8 ×4+4 ×2+8×2]

= 2 ×[32+8+16]

=2 ×56

=112 cm²

Volume of cuboid = L ×B×H

= 8 ×4×2

= 64 cm³

Volume of cube of side 1 cm = (Side)³=1³=1 cm³

So, number of cubes having volume 1 cm³ that can be cut from cuboid of volume 64 cm³ is given by =\frac{64}{1}=64=

1

64

=64

So, surface area of cube = 6(side)²=6 ×1×1=6 cm²

Surface area of 64 cubes each of side 1 cm = 64 ×6=384 cm²

Ratio of surface of original cuboid to the surface areas of all the unit cubes so formed =\frac{112}{384}=\frac{7}{24}=

384

112

=

24

7