A certain quantity of wood costs ₹250 per m³. A solid cubical block of such wood is bought for ₹182.25. Calculate the volume of the block and use the method of factors to find the length of one edge of the block.

Given,

Cost of 1 m³ wood = ₹250

By unitary method,

For ₹250, quantity of wood = 1 m³

For ₹182.25, quantity of wood = $\dfrac{182.25 \times 1}{250}$

= $\dfrac{18225}{25000}$

= $\dfrac{729}{1000}$

= 0.729 m³.

By formula,

Volume of cuboidal block = (side)³

∴ (side)³ = 0.729 m³

⇒ (side)³ = $\dfrac{729}{1000}$

⇒ side = $\sqrt[3]{\dfrac{729}{1000}}$

On factorising 729 and 1000 we get,

⇒ side = $\sqrt[3]{\dfrac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 5 \times 5 \times 5}}$

⇒ side = $\dfrac{3 \times 3}{2 \times 5} = \dfrac{9}{10}$ = 0.9 m.

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