Calculate the volume of the following objects:
(i) An iron sphere of mass 5 kg, the density of iron is 8200 $kgm ^{-3}$.
$(6.1\times 10^{-4} m^{3})$
(ii) 200 g of lead shot having density 11300 $kgm^{-3}$.
$(1.77\times10^{-5} m^{3})$
(iii) A gold bar of mass 0.2 kg. The density of gold is $19300 kg–^{-3}$.
$(1.04\times10^{-5} m^{3})$
Difficulty: Hard
Solution:
(i) Mass of iron sphere = m = 5 kg
Density of iron = $\rho$ = $8200 kgm^{-3}$
Volume of iron sphere = V =?
Volume =$\frac{Mass}{Density}$
Volume =$\frac{5}{8200}$
= 0.00060975 = $6.0975 \times10^{-4}$
Volume = $6.1\times 10^{-4}m^{3}$
(ii) Mass of lead shot = m = 200 g =$\frac{200}{1000}$ kg = 0.2 kg
Density of lead = $\rho$ = $11300 kgm^{-3}$
Volume of lead shot = V =?
Volume =$\frac{Mass}{Density}$
Volume =$\frac{0.2}{11300}$
= 0.000017699 = $1.76699 \times 10^{-5}$
Volume = $1.77 \times 10^{-5}m^{3}$
(iii) Mass of gold bar = m = 0.2 kg
Density of gold = $\rho$ = $19300 kgm^{-3}$
Volume of gold bar = V =?
Volume =$\frac{Mass}{Density}$
Volume =$\frac{0.2}{19300}$
= 0.000010362 = $1.0362\times 10^{-5}$
Volume = $1.04 \times 10^{-5}m^{3}$
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