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 ?
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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 ?
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Answer:
[tex]\huge\underline\bold {Given:} [/tex]
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.
[tex]\huge\underline\bold {Solution} [/tex]
Number of cubes
= Volume of cuboid/ Volume of cube
[tex] = \frac{8 \times 4 \times 2}{1 \times 1 \times 1} = 64[/tex]
Surface area of cuboid
[tex] = 2 \times (8 \times 4 + 4 \times 2 + 2 \times 8)cm {}^{2} \\ = 2 \times (32 + 8 + 16)cm {}^{2} \\ = 112cm {}^{2} [/tex]
Surface area of 64 cubes
[tex] = 64 \times 6cm {}^{2} = 384cm {}^{2} [/tex]
Therefore required ratio = 112/384
= 7/24
= 7 : 24.