TS EAMCET · Chemistry · Solid State

A cube of edge length $1 cm$ is divided into smaller cubes of uniform size of length $1 nm$ . Assuming that no voids are present, the ratio of total surface area of all the cubes of $1 nm$ edge length to the surface area of the initial cube is

A $10^{9}$
B $10^{7}$
C $10^{6}$
D $10^{5}$

Verified Solution

Answer & Solution

Correct Answer

(B) $10^{7}$

Step-by-step Solution

Detailed explanation

Surface area of cube of edge length 1cm =(6×1)cm2. Surface area of cube of edge length (1×10−7)cm=(6×10−14)cm2 Let n cubes of 6×10−14cm2 are present on dividing the cube of 6cm2 ∴n× volume of cube of edge length…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A cube of edge length 1 cm is divided into smaller cubes of uniform size of length 1 nm. Assuming that no voids are present, the ratio of total surface area of all the cubes of 1 nm edge length to the surface area of the initial cube is

Step-by-step Solution

A cube of edge length $1 cm$ is divided into smaller cubes of uniform size of length $1 nm$ . Assuming that no voids are present, the ratio of total surface area of all the cubes of $1 nm$ edge length to the surface area of the initial cube is