Question

If a metallic cuboid weighs 16 kg, how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original?

• A. $0.25kg$
• B. $0.50kg$
• C. $0.75kg$
• D. $1kg$

Answer 1

The correct option is A $0.25kg$

Let the original dimensions be $L,B,H$

The metallic cuboid weight depends on Volume and density of cuboid.

Here, Assuming the density is equally distributed,

Weight $\alpha$ Volume

Weight $=k\times$ Volume

Volume of the cuboid is $L\times B\times H=LBH$

$⟹16kg=kLBH\cdots \left(1\right)$

All the dimensions are reduced to one-Fourth

$l=\frac{L}{4}$

$b=\frac{B}{4}$

$h=\frac{H}{4}$

The new weight is given as $k\times l\times b\times h$

$⟹k\times \frac{L}{4}\times \frac{B}{4}\times \frac{H}{4}$

$⟹\frac{1}{64}\times kLBH$

From $\left(1\right)$

$⟹\frac{1}{64}\times 16=0.25kg$