The mass (kg) of benzene is about 4470 kg
This problem is about Density.
Density is the ratio of mass to the volume of the object.
[tex]\large {\boxed {\rho = \frac{ m }{ V } } }[/tex]
ρ = density of object ( kg / m³ )
m = mass of object ( kg )
V = volume of object ( m³ )
Given:
Diameter of Cylinder = d = 2.00 m
Radius of Cylinder = R = d/2 = 2.00/2 = 1.00 m
Length of Cylinder = L = 4.00 m
Liquid Depth = H = 0.85 m
Density of Benzene = ρ = 0.879 g/cm³ = 879 kg/m³
Unknown:
mass of benzene = m = ?
Solution:
This problem is about Liquid Volume in Partially Filled Horizontal Tanks
Firstly we will calculate the volume of Benzene by using following formula:
[tex]V = A \times L[/tex]
[tex]V = ( \texttt{Area of Sector - Area of Triangle} ) \times L[/tex]
[tex]V = [ R^2 \cos^{-1}(\frac{R - H}{R}) - (R - H)\sqrt {(2RH - H^2)} ] L[/tex]
[tex]V = [ 1^2 \cos^{-1}(\frac{1 - 0.85}{1}) - (1 - 0.85)\sqrt {(2(1)(0.85) - 0.85^2)} ] 4[/tex]
[tex]V = [ \cos^{-1} (0.15) - 0.15 \sqrt{ 0.9775} ] 4[/tex]
[tex]V \approx \boxed {5.0877 ~ m^3}[/tex]
[tex]m = \rho \times V[/tex]
[tex]m = 879 \times 5.0877[/tex]
[tex]m \approx \boxed {4470 ~ kg}[/tex]
Grade: High School
Subject: Mathematics
Chapter: Density
Keywords: Temperature , Density , Iron , Sphere , Volume , Mass
