Question

A solid cubical block of fine wood costs $Rs.256$ at $Rs.500$ per $m^3$. Find its volume and the length of each side.

Answer 1

Given: Total cost of wood $=Rs.256$

Rate $=Rs.500$ per $m^3$

$\therefore$ Volume of wood $=\frac{\text{Total cost}}{\text{Cost of 1}{m}^3}=\frac{256}{500}=0.512m^3$

$=0.512\times 100\times 100\times 100c{m}^3$ [$\because 1m=100cm$]

$=512000c{m}^3$

Let length of each side be ${}^{\prime }{a}^{\prime }$

then $a^3=512000=(80{)}^3$ [$\because$ Volume of cube $=(Side{)}^3$]

$\therefore a=80$

Hence length of each side is $80cm.$