Answer: a. m = 7.7 kg
b. V = 435.52 in³
c. m = 1927 kg
d. V = 335.37 cm³
e. m = 3 kg
Explanation: <u>Density</u> is the ratio of mass per volume, i.e., it's the measure of an object's compactness. Its representation is the greek letter ρ.
The formula for density is
![\rho=\frac{m}{V}](https://tex.z-dn.net/?f=%5Crho%3D%5Cfrac%7Bm%7D%7BV%7D)
Density's unit in SI is kg/m³, but it can assume lots of other units.
Some unit transformations necessary for the resolution of the question:
1 L = 1 dm³ = 1000 cm³
1 in³ = 16.3871 cm³
1 g = 0.001 kg
a. V = 1.34 L = 1340 cm³
![\rho=\frac{m}{V}](https://tex.z-dn.net/?f=%5Crho%3D%5Cfrac%7Bm%7D%7BV%7D)
![m=\rho.V](https://tex.z-dn.net/?f=m%3D%5Crho.V)
m = 5.75 * 1340
m = 7705 g => 7.705 kg
Mass of object 1 with volume 1.34L is 7.7 kg.
b. A cube's volume is calculated as V = side³
V = 7.58³
V = 435.52 in³
Volume of object 2 is 435.52 in³.
c. Using 1 in³ = 16.3871 cm³ to change units:
V = 435.52 * 16.3871
V = 713689.4 cm³
Then, mass will be
![m=\rho.V](https://tex.z-dn.net/?f=m%3D%5Crho.V)
m = 2.7 * 713689.4
m = 1926961.4 g => 1927 kg
Mass of object 2 is 1927 kg.
d. Volume of a sphere is calculated as ![V=\frac{4}{3}.\pi.r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D.%5Cpi.r%5E%7B3%7D)
Diameter is twice the radius, then r = 4.31 cm.
Volume is
![V=\frac{4}{3}.\pi.(4.31)^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D.%5Cpi.%284.31%29%5E%7B3%7D)
V = 335.37 cm³
Volume of object 3 is 335.37 cm³.
e. ![m=\rho.V](https://tex.z-dn.net/?f=m%3D%5Crho.V)
m = 8.96 * 335.37
m = 3004.91 g => 3 kg
Mass of object 3 is 3 kg.