Question

Shyam wants to make a sold brick shape structure from $400$ wooden cubes of unit volume each. If the sides of the solid brick have the ratio $1:2:3$, then the maximum number of cubes, which can be used will be

• A. $400$
• B. $288$
• C. $300$
• D. $384$

Answer 1

Answer: (D)

$384$

Let 4he side are $x,2x,3x$
$v=\left(x\right)\left(2x\right)\left(3x\right)=6x^3$
$ATQ$ $6x^3\le 400\Rightarrow x^3\le 66\frac{2}{3}\Rightarrow x=64$
$\therefore$ $x=64$
maximum number of cubes $=6x^3=6\times 64=384$