A certain quantity of wood costs ₹ 25,000 per m³. A solid cubical block of such wood is bought for ₹ 18,225. Calculate the volume of the block and use the method of factor to find the length of one edge of the block.

Given,

Cost of 1 m³ wood = ₹ 25,000

Cost of a solid cubical block = ₹ 18,225

As we know that, cost of a solid cubical block = volume of block x cost of 1 m³ wood

$\text{Volume of block }= \dfrac{\text{Cost of a solid cubical block}}{\text{Cost of wood per m}^3}\\[1em] = \dfrac{18225}{25000}\\[1em] = \dfrac{18225}{25000}\\[1em] = \dfrac{729}{1000}\\[1em] = 0.729$

By formula,

Volume of cuboidal block = (side)³

∴ (side)³ = 0.729 m³

$\Rightarrow \text{(side)}^3 = \dfrac{729}{1000}\\[1em] \Rightarrow \text{side} = \sqrt[3]{\dfrac{729}{1000}}\\[1em]$

On factorising 729 and 1000 we get,

$\Rightarrow \text{side} = \sqrt[3]{\dfrac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 5 \times 5 \times 5}}\\[1em] \Rightarrow \text{side} = {\dfrac{3 \times 3}{2 \times 5}}\\[1em] \Rightarrow \text{side} = {\dfrac{9}{10}}\\[1em] \Rightarrow \text{side} = 0.9$

Hence, volume of block = 0.729 m³ and the length of one edge of the block is 0.9 m.