Question

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

• A. 60
• B. 80
• C. 20
• D. 22

Answer 1

Answer: (C)

Total surface area of eight cubes

$=8\times 6\times \left(\frac{1}{2}\times \frac{1}{2}\right)$

Apply the formula

Surface area on $n$ split of a

$=8^n\times 6\times {\left(\frac{1}{2}\right)}^{2n}$

$6291456=8^n\times 6\times {\left(\frac{1}{2}\right)}^{2n}$

$n$ cubes of $xcm$ surface are $6x^2=6291456$

$x^2=1048576$

$\therefore 2^y=1048576$

$y=20$