A solid cubical block of fine wood costs ₹256 at the rate of ₹500/m${}^3$. Find the length of each side.

1. 90 cm

2. 80 cm

3. 70 cm
4. 120 cm

The correct option is B

80 cm

Let the edge length of the cubical box be 'a' m.

Given, ₹500 is the cost of 1 m${}^3$ of wood.

Then, ₹256 is the cost of $\left(\frac{256}{500}\right)m^3$ of the wood, which is $0.512m^3$ of the wood.

So, volume of the total wood = $0.512m^3$

Volume of the cube = $a^3$
$a^3=0.512m^3\Rightarrow a=0.8m$

Hence, length of each side of the cubical block of wood is 80 cm.