Finely divided catalyst has greater surface area and has greater catalytic activity than the compact solid. If a total surface area of 6291456 `cm^(2)` is required for adsorption in a catalytic gaseous reaction, then how many splits should be made in a cube of exactly 1 cm in length to achieve required surface area?
[Given : One split of a cube gives eight cubes of same size]

Options

A. 60
B. 80
C. 20
D. 22

Answer

C

Explanation

Total Surface area of eight cubes `=8xx6xx(1/2xx1/2)^2`
Apply the formula
Surface area on n split of a cube `=8^nxx6xx(1/2)^(2n)`
`6291456=8^n xx 6 xx (1/2)^(2n)`