Answer:
(i) 0.2 kg
(ii) kg/cm³
(b) 2.29 kg
Step-by-step explanation:
This problem gives you relations between units, and the formulas for density and mass. It is asking you to make use of these relations in various mass and density calculations.
<h3>(a)(i)</h3>
The relationship between kg and pounds can be used to write a units conversion multiplier. It will have numerator equal to denominator, but will have units such that multiplying by it will give the units you want.
0.44 pounds × multiplier = __ kg
0.44 pounds × (1 kg)/(2.2 pounds) = (0.44/2.2)(1 kg)
0.44 pounds = 0.2 kg
__
<h3>(a)(ii)</h3>
The formula can be used to find the units of interest:
Density = mass/volume
units of density = (units of mass)/(units of volume)
units of density = kg/cm³
__
<h3>(b)</h3>
Using the given formula with the given value of L, we find the volume to be ...
V = 4(1.40 cm)(3 -1.40 cm)² = 14.336 cm³
Then the mass is ...
mass = volume × density
mass = (14.336 cm³)×(0.160 kg)/(1 cm³) = 2.29376 kg
The mass is about 2.29 kg.
_____
<em>Additional comment</em>
Often you will see density in terms of kg/m³ or g/cm³. Water has a density of about 1 g/cm³ or 1000 kg/m³. The most dense non-radioactive element in the periodic table is osmium, with a density of about 22.6 g/cm³, or 0.0226 kg/cm³. The material in part (b) of this problem has a density about 7 times that, so is clearly not from Earth.
