Question

In an arbitrarily chosen system of units and measurements, area was taken as a fundamental quantity and one unit area, denoted as A, is defined as the total surface area of a cube of unit length as its side. Find the unit of length in terms of A in this system.

• A. $\sqrt{\frac{A}{6}}$
• B. $\frac{A}{6}$
• C. $\sqrt{A}$
• D. $\sqrt{\frac{A}{2}}$

Answer 1

The correct option is A $\sqrt{\frac{A}{6}}$

Let the length of the cube be $l$

So, the total surface area of a cube is represented as:

$A=6l^2$

$⟹l=\sqrt{\frac{A}{6}}$