The density of a material, in the shape of a cube, is determined by...

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are

1 . 5 %

and

1 %

, respectively, the maximum error in determining the density is:

Options

A $6 %$
B $2.5 %$
C $3.5 %$
D $4.5 %$

Correct answer

D. $4.5 %$

Step-by-step solution

ρ = \dfrac{M}{L3}⇒ \dfrac{\Deltaρ}{ρ} = \dfrac{\Delta M}{M} + \dfrac{3\Delta L}{L}⇒ \dfrac{\Deltaρ}{ρ} \times 100 = 1.5 + 3 \times 1

%

~relative error,

= 4.5%

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