The length l, breadth b and thickness t of a | vedclass

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Question

Volume, $V = lbt$

The $\%$ error in volume $ = \,\,\frac{{\Delta \ell }}{\ell }\,\, 	imes \,\,\,100\,\, + \,\,\frac{{\Delta b}}{b}\,\, 	imes

Vedclass · Accepted Answer

$0.36$

Vedclass · Answer

Volume, $V = lbt$

The $\%$ error in volume $ = \,\,\frac{{\Delta \ell }}{\ell }\,\, 	imes \,\,\,100\,\, + \,\,\frac{{\Delta b}}{b}\,\, 	imes \,\,100\,\, + \frac{{\Delta t}}{t}\,\, 	imes \,\,100$

$ = \,\,\frac{{0.01}}{{15.12}}\,\, 	imes \,\,100\,\, + \;\,\frac{{0.01}}{{10.15}}\,\, 	imes \,100\,\, + \,\,\frac{{0.01}}{{5.28}}\,\, 	imes \,\,100$

$ = \,\,0.07\,\, + \;\,0.10\,\, + 0.19\,\, = \,\,0.36$

The length $l$, breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $l=15.12 \pm 0.01\; cm , t =5.28 \pm 0.01 \;cm$ $b =10.15 \pm 0.01\; cm$. The percentage error in volume upto proper significant figures is

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