If a cube of edge length 1.00 cm is sub divided into colloidal size cubes, each having an edge length of 1 0 − 6 cm , what would be the total surface area of these colloidal size cubes ? ( lo g 2 = 0.

Question

If a cube of edge length 1.00 cm is sub divided into colloidal size cubes, each having an edge length of 1 0 − 6 cm , what would be the total surface area of these colloidal size cubes ? ( lo g 2 = 0.30 )

TestHub · Accepted Answer

Every division gives 8 identical cubes

in first step

Edge length of cube $= \frac{1}{2} cm$

no. of cube $= 8$

in second step edge length of cube $= (\frac{1}{2})^{2}$

no. of cube $= 8^{2}$

for nth step

edge length

no. of cube $= (8)^{n}$

$(\frac{1}{2})^{n} = 1 0^{- 6}$

$- n lo g 2 = - 6 lo g 10$

$n = 6/0.30 = 20$

So, $n = 20$

edge length of each colloid $= (\frac{1}{2})^{20}$

no. of cube $= (8)^{20}$

surface area of one colloid $= 6 a^{2}$

$= 6 [(\frac{1}{2})^{20}]^{2}$

$= 6 \times (\frac{1}{2})^{40}$

Total surface area $=$ no of cubes $x$ surface area of each cube

$= (8)^{20} \times 6 \times (\frac{1}{2})^{40}$

$= 6 \times 1 0^{6}$

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