Question

The area of three adjacent faces of a cube is a, b and c. The volume is V. What is the appropriate relation between V and a, b, c?

• A. $V^4=abc$
• B. V = abc
• C. $V^3=abc$
• D. $V^2=abc$

Answer 1

The correct option is D $V^2=abc$

Let x be side of the cube.
Area of each face of the cube $=x^2$
Given: area of three adjacent faces are $a^2$, $b^2$ and $c^2$
$\Rightarrow a^2=b^2=c^2=x^2$
Now, volume of cube, $V=x\times x\times x$
$V=\sqrt{a}\times \sqrt{b}\times \sqrt{c}$
$\Rightarrow V^2=abc$