Respuesta :
density=mass/volume
The volume of a sphere is:
V=(4πr^3)/3 so
d=3m/(4πr^3), we are given that r=2cm and m=12g
d=36/(32π) g/cm^3
d=1.125/π g/cm^3
d≈0.358 g/cm^3
d≈0.36 g/cm^3 (to nearest hundredth of a gram per cm^3)
The volume of a sphere is:
V=(4πr^3)/3 so
d=3m/(4πr^3), we are given that r=2cm and m=12g
d=36/(32π) g/cm^3
d=1.125/π g/cm^3
d≈0.358 g/cm^3
d≈0.36 g/cm^3 (to nearest hundredth of a gram per cm^3)
The density of the sphere with mass 12 g and radius 2 cm is 0.36 g/cm³. The correct option is the first one (0.36 g/cm3)
From the question,
The mass of the sphere is 12 g and
The radius is 2 cm.
To determine its density,
From the formula
[tex]Density =\frac{mass}{volume}[/tex]
Therefore, we will first determine the volume of the sphere.
Volume of a sphere is given by the formula
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Where [tex]V[/tex] is the volume of the sphere
and [tex]r[/tex] is the radius of the sphere
Take [tex]\pi = 3.14159[/tex]
From the question, [tex]r = 2 \ cm[/tex]
Put these values into the equation,
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
[tex]V = \frac{4}{3}\times 3.14159 \times 2^{3}[/tex]
[tex]V = \frac{4}{3}\times 3.14159 \times 8[/tex]
[tex]V = \frac{100.53088}{3}[/tex]
[tex]V = 33.51029 \ cm^{3}[/tex]
Now, for the density
Put the values of the volume and mass in the equation
[tex]Density =\frac{mass}{volume}[/tex]
From the question, mass = 12 g
From above, V = 33.51029 cm³
∴ [tex]Density =\frac{12 \ g}{33.51029 \ cm^{3} }[/tex]
[tex]Density = 0.3581 \ g/cm^{3}[/tex]
Density ≅ 0.36 g/cm³
Hence, the density of the sphere with mass 12 g and radius 2 cm is 0.36 g/cm³. The correct option is the first one (0.36 g/cm3)
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