A solid cubical box of fine wood costs $R s . 256$ at the rate $R s . 500 / m^{3}$ . Find its volume and length of each side.

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Solution

solid cubical box of fine wood costs $R s . 256$ at the rate $R s . 500 / m^{3}$

Cost for one meter cube = $R s . 500$

Original Cost = $R s . 256$

Volume $\times$ cost for one meter cube = $256$

volume = $\frac{256}{500}$ = $0.512 m^{3}$

Volume of Cube = $l^{3}$ ( $l$ is the side)

$l^{3}$ = $0.512 m^{3}$

Hence $l = \sqrt[3]{0.512} = 0.8 m$

The length of the side is $80$ cm

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