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(D) The density $\rho$ of a cube is given by the formula $\rho = \frac{M}{V} = \frac{M}{L^3}$,where $M$ is the mass and $L$ is the length of the side

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) The density $ho$ of a cube is given by the formula $ho = \frac{M}{V} = \frac{M}{L^3}$,where $M$ is the mass and $L$ is the length of the side of the cube.Using the formula for relative error,the maximum percentage error in density is given by:$\frac{\Delta ho}{ho} 	imes 100 = \frac{\Delta M}{M} 	imes 100 + 3 	imes \left( \frac{\Delta L}{L} 	imes 100 ight)$Given that the maximum error in mass $\frac{\Delta M}{M} 	imes 100 = 3\%$ and the maximum error in length $\frac{\Delta L}{L} 	imes 100 = 2\%$.Substituting these values into the equation:$	ext{Percentage error in } ho = 3\% + 3 	imes (2\%) = 3\% + 6\% = 9\%$.Therefore,the maximum error in the measurement of the density of the cube is $9\%$.

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively,then find the maximum error in the measurement of the density of the cube.

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