Question

A solid cubical block of fine wood costs rupees 256 at rupees 500 per mº. Find its volume and the
length of each side.​

Answer 1

$\sf{\underline{\underline{Given:}}}$

$\sf{Cost\:of\:one\:meter\:cube\:of\:the\:block= Rs.\:500.}$

$\sf{Original\:Cost = Rs. 256.}$

$\sf{\underline{\underline{Now:}}}$

$\sf\red{Volume = \dfrac{Original\:cost}{Cost\:of\:one\:meter\:cube}}$

$\sf\purple{ \: \: \: \: \: \: \: = \dfrac{250}{500}}$

$\sf\green{ \: \: \: \: \: \: \: = 0.5\:{m}^{2}}$

$\sf{\underline{\underline{We\:know\:that:}}}$

$\sf\orange{ Volume\: of\:Cube = {A}^{3} \: \: (A\: denotes\:side)}$

$\sf{\underline{\underline{SoLUTiON:}}}$

$\sf\purple{\implies {A}^{3} = 0.5}$

$\sf\red{\implies A = \sqrt[3]{0.5}}$

$\sf\green{\implies A\:(side) = 0.8}$

$\sf{\underline{\underline{Therefore:}}}$

$\sf\red{The\:Length\:of\:each\:side = 0.8\:m}$

$\sf\orange{ Volume = 0.5\:{m}^{3} }$