Question

The mass of a solid cube is 856 g, and each edge has a length of 5.35 cm. Determine the density ρ of the cube in basic SI units.

Answer 1

Answer:

Because 1 \mathrm{~g}=10^{-3} \mathrm{~kg}1 g=10

−3

kg and 1 \mathrm{~cm}=10^{-2} \mathrm{~m}, 1 cm=10

−2

m, the mass mm and volume VV in basic SI units are

m=856 \mathrm{~g} \times 10^{-3} \mathrm{~kg} / \mathrm{g}=0.856 \mathrm{~kg}m=856 g×10

−3

kg/g=0.856 kg V =L^{3}=\left(5.35 \mathrm{~cm} \times 10^{-2} \mathrm{~m} / \mathrm{cm}\right)^{3}V=L

3

=(5.35 cm×10

−2

m/cm)

3

=(5.35)^{3} \times 10^{-6} \mathrm{~m}^{3}=1.53 \times 10^{-4} \mathrm{~m}^{3}=(5.35)

3

×10

−6

m

3

=1.53×10

−4

m

3

Therefore,

\rho=\frac{m}{V}=\frac{0.856 \mathrm{~kg}}{1.53 \times 10^{-4} \mathrm{~m}^{3}}=5.59 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}ρ=

V

m

=

1.53×10

−4

m

3

0.856 kg

=5.59×10

3

kg/m

3