Question

A solid cubical block of fine wood costs Rs256 at Rs 500 per m2 . find its volume & the length of each side.

Answer 1

Answer:

Volume = $\frac{512}{625\sqrt5}m^3$

Length of each side = $\frac{8}{5\sqrt5} m$

Step-by-step explanation:

If the solid cube costs $\frac{Rs500}{m^2}$, then Rs256 gives us $\frac{\frac{Rs500}{500} }{\frac{1m^2}{500} } = \frac{Rs1}{\frac{1}{500}m^2 } = \frac{(Rs1)(256)}{(\frac{1}{500}m^2)(256) } = \frac{Rs256}{\frac{64}{125}m^2 } = \sqrt{\frac{Rs256}{\frac{64}{125}m^2 } } = \frac{Rs16}{\frac{8}{5\sqrt5}m }$. Thus, $\frac{8}{5\sqrt5} m$ is the length of its side, and its cube gives us $\frac{512}{625\sqrt5}m^3$ to be its volume.

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