Question

A cuboid of size 8 cm × 4 cm × 2 cm is cut into cubes of equal size of 1 cm side. What is the ratio of the surface area of all the unit cubes so formed ?​

Answer 1

Answer:

$\huge\underline\bold {Given:}$

Size of the cube = 8 cm × 4 cm × 2 cm

It is cut into cubes of equal size of 1 cm side.

To find:

Ratio of the surface area of all the unit cubes formed.

$\huge\underline\bold {Solution}$

Number of cubes

= Volume of cuboid/ Volume of cube

$= \frac{8 \times 4 \times 2}{1 \times 1 \times 1} = 64$

Surface area of cuboid

$= 2 \times (8 \times 4 + 4 \times 2 + 2 \times 8)cm {}^{2} \\ = 2 \times (32 + 8 + 16)cm {}^{2} \\ = 112cm {}^{2}$

Surface area of 64 cubes

$= 64 \times 6cm {}^{2} = 384cm {}^{2}$

Therefore required ratio = 112/384

= 7/24

= 7 : 24.

Answer 2

Answer:

7:24

Step-by-step explanation:

Number of cubes =

Volumeofcube

Volumeofcuboid

=

1×1×1

8×4×2

=64

Surface area of cuboid =2×(8×4+4×2+2×8)cm

2

=2×(32+8+16)cm

2

=112cm

2

Surface area of 64 cubes =64×6cm

2

=384cm

2

∴ Required ratio =

384

112

=

24

7

=7:24