Question

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 catalysed gaseous reaction, then how many splits should be made to 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)

• 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

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

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

$n$ cubes of $x\, cm$ surface are $6 x^{2}=6291456$

$x^{2}=1048576$

$\therefore 2^{y}=1048576$

$y=20$