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:

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=164=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}=384112=247